When the Cuban Revolution took place in 1958 and Fidel Castro declared himself to be a communist, the United States took notice. Cuba would be, then, the first communist nation in the Western Hemisphere. We dusted off the Monroe Doctrine and the Roosevelt Corollary and attempted to enforce containment by quickly removing Castro from power. So cause #1 was the Revolution and our policy of containment. This led to the Bay of Pigs attempted reinvasion of Cuba, a dismal failure that only strengthened Castro's resolve and indirectly led to conflict #2.
Nikita Krushchev decided that his communist foothold needed to be protected with nuclear weapons so that invasion would become impossible, so over Castro's objections, he convinced the leader to allow them to be stationed there. This was cause of conflict #2, the Cuban Missile Crisis, where for 13 days in October of 1962, the two superpowers squared off for what seemed like a probable nuclear war.
Also remember that because of the revolution, we have had an embargo on Cuba for over 50 years, and the CIA also tried to assassinate Castro on numerous occasions.