It’s well known that the former US president, Richard Nixon, carpet-bombed Cambodia, spewed out anti-Semitic slurs and crude misogynistic jokes in the White House and smeared his political opponents with ruthless “dirty tricks” campaigns.

And nobody forget Richard Nixon lied to his country about his involvement in the Watergate scandal and went down in history as America’s shiftiest, darkest President.

Given everything that Richard Nixon has been accused of, it’s difficult to believe there could be any more skeletons left in his cupboard. But it seems there are.

A new biography of Richard Nixon, written by Don Fulsom, a veteran Washington reporter who covered the former president years, suggests the 37th U.S. President had a serious drink problem, beat his wife and – by the time he was inaugurated in 1969 – had links going back two decades to the Mafia, including with New Orleans godfather Carlos Marcello, then America’s most powerful mobster.

Yet the most extraordinary claim is that the homophobic Richard Nixon may have been gay himself. If true, it would provide a fascinating insight into the motivation and behavior of a notoriously secretive politician.

Don Fulsom argues that Richard Nixon may have had an affair with his best friend and confidant, a Mafia connected Florida wheeler-dealer named Charles “Bebe” Rebozo who was even more crooked than Nixon.

The book, “Nixon’s Darkest Secrets”, is out next month – by coincidence at the same time as the UK release of a new film directed by Clint Eastwood about another supposed closet gay among Washington’s 20th-century hard men.

But while FBI boss J. Edgar Hoover, played in Eastwood’s film by Leonardo DiCaprio, allegedly had an affair with his squeaky-clean deputy Clyde Tolson, Richard Nixon’s supposed secret paramour was a very different character.

Bebe Rebozo was a short, swarthy, good-looking Cuban-American businessman with a history of failed relationships with women and close alliances with Miami’s Mafia chiefs.

The veteran TV newsman Dan Rather recalled how Bebe Rebozo “transmitted the sense of great sensuality”, paying tribute to his “magnetic” personality and “beautiful eyes”.

Don Fulsom uses recently revealed documents and eyewitness interviews – including with FBI agents – to shed new light on long-standing suspicions among White House insiders that Richard Nixon may have been more than just good buddies with Bebe Rebozo.

The journalist claims Richard Nixon’s relationship with Pat, his wife of 53 years, was little more than a sham. A heavy drinker whom his own staff dubbed “Our Drunk”, Richard Nixon used to call his First Lady a “f***ing bitch” and beat her before, during and after his presidency, says Don Fulsom.

Richard Nixon and his wife had separate bedrooms at the White House – and in Key Biscayne, the exclusive resort near Miami where they holidayed, Pat Nixon didn’t even sleep in the same building. Bebe Rebozo, however, was in the house next door.

Don Fulsom claims one of Richard Nixon’s former military aides had a secret job “to teach the President how to kiss his wife” so they would look like a convincing couple.

How much of this can we believe? Richard Nixon died in 1994 and his reputation is pretty much irredeemable. As with Eastwood’s Hoover film, there is no definitive proof, but plenty of “supporting evidence”.

Don Fulsom quotes a former Time magazine reporter who, at a Washington dinner, bent down to pick up a fork and saw the two holding hands under the table. It was, the reporter judged, sufficiently intimate to suggest “repressed homosexuality”.

Another journalist related how, loosened up by drink, Richard Nixon once put his arm around Bebe Rebozo “the way you’d cuddle your senior prom date. Something was fishy there”.

But who exactly was Bebe Rebozo, and how did a shady Florida businessman of unclear sexual leanings end up as the bosom friend of one of the most paranoid and buttoned-up political leaders of the 20th century?

Born two months before Richard Nixon in 1912, Charles Gregory Rebozo was the son of a Cuban cigar-maker and, as the youngest of nine, was stuck with the nickname “Bebe”.

Bebe Rebozo came from poverty but worked his way up through property speculation and then banking. According to the FBI, he had close links with Mob bosses such as Santo Trafficante, the Tampa Godfather, and Alfred “Big Al” Polizzi, a stooge of Meyer Lansky, the Cosa Nostra’s financial brains.

By the 1960s, an FBI agent was describing Bebe Rebozo as a “non- member associate of organized crime figures”. He bought land in Florida with a business partner who was believed to be a front for some of the most powerful Mafiosi.

When Bebe Rebozo started his own bank in Florida in 1964, Richard Nixon – then a lawyer – wielded a golden shovel at the ground-breaking ceremony and became its first depositor.

According to Mafioso Vincent Teresa, the bank was used by the Mob to launder stolen cash. It hardly seems possible that Richard Nixon, who pledged to make fighting organized crime a priority of his presidency, could not have known of his best friend’s Mafia links.

Richard Nixon had just won one of California’s U.S. Senate seats when he first met Bebe Rebozo in 1950. Fearing Richard Nixon was facing a nervous breakdown, fellow Senator George Smathers suggested a holiday in Florida and enlisted his old school friend Bebe Rebozo to show the socially awkward Nixon a good time.

Their first jaunt together – in Bebe Rebozo’s 33ft fishing boat – did not go well. Bebe Rebozo later complained that Richard Nixon just sat reading papers and, according to his host, barely said half a dozen words to him.

George Smathers said Bebe Rebozo later told him: “Don’t ever send that son of a bitch Nixon down here again. He’s a guy who doesn’t know how to talk, doesn’t drink, doesn’t smoke, doesn’t chase women… he can’t even fish.”

But Bebe Rebozo persevered – and according to a cynical George Smathers, Richard Nixon’s rising stardom in Washington and the potential influence it offered “had a lot to do with it”.

In months, Richard Nixon and Bebe Rebozo were inseparable, holidaying with Nixon’s wife Pat – and without her. Bebe Rebozo became an “uncle figure” to the Richard Nixons’ two daughters, Tricia and Julie. The dapper Cuban-American chose Richard Nixon’s clothes and even selected the films he watched at the White House.

On Richard Nixon’s solo visits to Key Biscayne, they swam and sunbathed, indulging in their shared passions for discussing Broadway musicals and barbecuing steaks.

Both men were also extremely secretive, and their relationship – described as the “most important unsolved mystery in Nixon’s life” – was kept so discreet that the New York Times did not mention it for nearly 20 years.

Observers noticed their intimacy became most apparent when they were drunk. An aide recalled them playing a game called King of the Pool at Key Biscayne: “It was late at night, the two men had been drinking. Nixon mounted a rubber raft in the pool while Rebozo tried to turn it over. Then, laughing and shouting, they’d change places.”

They were seen together at the same British-themed hostelries in the Key: the English Pub, where they drank beer from tankards engraved with their names, and the Jamaica Inn, where they ate at a discreet booth.

Both spots were owned by another businessman with Mob links and the secret service asked Richard Nixon to find another place to eat.

Why the President’s minders didn’t raise alarms about Bebe Rebozo’s Mafia connections has puzzled experts, but they probably didn’t dare. When a New York newspaper investigated Bebe Rebozo’s Mob links in the 1970s, its staff suddenly found themselves under secret service surveillance.

A White House aide once dismissed Bebe Rebozo’s role as “the guy who mixed the Martinis”, but he was far more important than that.

When Richard Nixon became President, Bebe Rebozo got his own office and bedroom at the White House, and a security clearance that allowed him to go in and out without being logged by the secret service. Using a false name, says Don Fulsom, Bebe Rebozo even got into Richard Nixon’s hotel suite during a trip to Europe.

The President’s closest colleagues complained at the way Bebe Rebozo monopolized Richard Nixon’s time. General Alexander Haig, his last chief of staff, is said to have imitated Bebe Rebozo’s “limp wrist” manner and joked that Rebozo and Nixon were lovers.

According to Don Fulsom, Henry Kissinger resented the way Bebe Rebozo would fly on Air Force One, the Presidential plane, wearing a blue U.S. Navy flight jacket bearing the President’s seal and with his name stitched on it.

Away from Richard Nixon’s side, Bebe Rebozo surrounded himself with glamorous women and threw Miami parties that descended into orgies, but was it all a front?

Aged 18, Bebe Rebozo reportedly enjoyed an “intense” affair with a young man, Donald Gunn. He later wed Donald Gunn’s teenage sister. The marriage lasted four years and, according to his wife, was never consummated.

Bebe Rebozo didn’t marry again until middle age, when he entered what Newsweek magazine described as an “antiseptic” alliance with his lawyer’s secretary. “Bebe’s favourites are Richard Nixon, his cat – and then me,” the lady complained later. A fellow Miami resident told Richard Nixon biographer Anthony Summers that Bebe Rebozo was definitely part of the city’s gay community.

Anthony Summers and co-writer Robbyn Swan, however, question whether there is enough evidence to suggest Richard Nixon was gay. “They held hands on occasion, and both men had problems with consummating physical relationships with women, but we found no evidence that Nixon was actively homosexual,” Anthony Summers said.

Physical or not, Richard Nixon’s attraction to Bebe Rebozo has struck many as politically reckless. Nixon expert Professor Fawn Brodie couldn’t understand how he would be “willing to risk the kind of gossip that frequently accompanies close friendship with a perennial bachelor”. After all, Fawn Brodie added, Nixon was, in public, a virulent gay-hater.

When Walter Jenkins, a trusted aide to President Lyndon Johnson, was caught providing sexual favors to a retired sailor in a YMCA lavatory, Richard Nixon denounced him as “ill”. People who suffered this “illness”, he added, “cannot be in places of high trust”.

Bebe Rebozo was certainly in a position of “high trust”, and not only because he was a key fundraiser. He was with Richard Nixon when he announced his successful run for President and again in June 1972 when Nixon learned that five men hired by the White House to break into the Watergate building had been arrested.

“We were swimming at Key Biscayne in front of my house,” Bebe Rebozo recalled.

“They came out and told him. He said: <<What in God’s name were they doing there?>> We laughed and forgot about it.”

Bebe Rebozo also ended up being investigated by the Watergate committee, which found that a $100,000 cash contribution from the industrialist Howard Hughes that was meant for the Republican Party was actually in Rebozo’s safe deposit box.

It also emerged that both Richard Nixon and Bebe Rebozo’s personal wealth had soared during Nixon’s first five years in the White House, Rebozo’s rising nearly seven-fold from $675,000 to nearly $4.5 million.

Bebe Rebozo escaped prosecution – allegedly because of a White House deal – and he stood by his disgraced friend. He was at Nixon’s bedside during his final days.

When Bebe Rebozo died in 1998, he left more than $19 million to the Nixon memorial library, whose executive director eulogized him as a “consummate gentleman” on whose “wise counsel, shrewd political insight and ready wit” Richard Nixon relied.

Typically, Richard Nixon had been rather less charitable – he always described Bebe Rebozo as just a “golfing partner”.