The Soviet Union, after its revolution, became the world's first Communist country. From the days even before order was established, the United States had been trying to combat and destroy it.
After Cuba's relations with the United States worsened, the Soviet Union happily filled the void, supplying Cuba with economic assistance, trade, and military support.
President Eisenhower then strengthened the embargo. He also refused to pay for the sugar Cuba had been guaranteed to sell to the United States. When this happened, the Soviets agreed to buy the sugar and Cuba became more closely aligned with the Soviet Union.
The Bay of Pigs invasion ended the possibility of a US-Cuba friendship. Fidel Castro decided to allow the Soviet Union to deploy nuclear missiles in Cuba and aid Cuba in its defense.
This prompted the Cuban Missile Crisis, which ended poorly for the Soviets.
The Cuban Government attempted numerous economic programs that failed. They were forced to turn largely to the Soviet Union and adopt its economic system.
The Soviet also heavily supported Cuba. Half of Soviet aid to the Third World was given to Cuba. Cuba received about US $3 billion per year in aid, which it used to fund its social programs.
When the Soviet Union and Eastern Europe were beginning to fall apart, Cuba showed it would not. The end of Soviet bloc trade, which had accounted for 84% of Cuban trade, hurt the Cuban economy terribly.