re you talking about when they became independent from Spain?
One of the big disadvantages is that there was then a series of power struggles to see who would run the country, and in the Cuban revolution in the late 1950's, Fidel Castro came to power.
His way of running the country under a strict Socialist/Communist government made much of the rest of the world so angry, that many countries refused to trade with Cuba or have anything to do with them in international relations.
The result of that was that Cuba became economically very poor, and politically very cut-off from a lot of the world.
So that was one long-term disadvantage of being independent from Spain.
It's a really complex issue. Do you have books or articles that you've been reading about Cuba?