Yes, American mobsters did have substantial investments in Cuba.

First a note on terminology. Following Joseph Albini, I’ll say that it’s wise to focus on the mob not as an organization, but as a system of relationships. While it was indeed “organized: crime, it wasn’t necessarily as well-defined and rigidly hierarchical as, say the Coca-Cola company or the New York Police Department. It’s more a loosely organized group of operators who have sometimes-complimentary investments in a variety of operations, rather than a cohesive corporation that wholly owns its subsidiaries. Mob bosses and associates invested their own money and looked out for their interests, rather than managing the capital and operations of an independent corporate entity.

So I wouldn’t say “mafias” had interests in Cuba. Rather, I would say that individuals alleged to be members of the Mafia, or La Cosa Nostra, had substantial interests there. Mobsters’ many connections to Cuba were fictionalized in The Godfather 2, with Hyman Roth standing in for real-life mob financier Meyer Lansky. Lansky’s investment in Havana’s Riviera hotel (and casino) were sufficient that his heirs have pressed the Cuban government for compensation, due to the nationalization of the Riviera after the communist takeover.

Investing in Havana was consistent with the investment patterns of American illegal gambling operators going back to the mid-19th century. Traditionally, most operations were owned by syndicates of investors, with the major shareholder usually serving as on-site manager (source is my own Roll the Bones: The History of Gambling). When a single illicit casino might be forced to shut down due to government pressure or an actual raid, it made sense to diversify one’s holdings. So you had John Morrissey owning faro houses in both New York City and Saratoga Springs and, later, Richard Canfield having interests through the New England and New York areas. Lansky raised this to an art form, with interests in various enterprises throughout the United States and Caribbean.

Some evidence of the scope of American gambling interests in Havana is that the city entered the public consciousness as a place for Americans who liked gambling to visit. For example, at the end of Guys and Dolls (film 1955, Broadway play 1950, based on Damon Ruynon stories of the 1920s/1930s), Sky Masterson takes Sarah Brown to dinner in Havana, Cuba—implying that degenerate gamblers like Masterson and Nathan Detroit would be familiar enough with that town to know of the restaurants there, and they wouldn’t just be attracted by the climate. Ten years later, the dinner would probably be in Las Vegas.

In short- Yes!

Currently we view Cuba as a "we don't really go there" country, but pre-revolution, it was considered to be a common vacation spot. It's proximity to the US made it an easy destination travel, and was kind of a "Vegas before there was Vegas", with the added benefit of beaches, etc.

Before the revolution, the Cuban government (under Batista) gave foreign nationals very lucrative terms if they would buy and develop properties. The Mafia saw this as a way to build casinos at a fairly cheap cost, with the additional benefit of a friendly government that would less likely regulate them out of existence. From a practical perspective, this involved suitcases full of cash being donated to government officials, to get them to sign off on contracts, look the other way, etc.

Coming to the revolution, the common man in Cuba began to see the alliance between the government and the Mafia as a basic wholesale looting of the country. While some people got casino jobs, the truth was most people just saw the money flowing up and out.