No, Cuba is not a state, it is a country, so it does not have a
state capitol building.
The capital city of Cuba is Havana.
El Capitolio, or National Capitol Building in Havana, Cuba, was
the seat of government in Cuba
until after the Cuban Revolution in 1959, and is now home to the
Cuban Academy of Sciences.
"El Capitolio" has a size of 681 by 300 ft. Its design and name
recall the United States Capitol
in Washington, D.C.. Completed in 1929, it was the tallest
building in Havana until the 1950s
and houses the world's third largest indoor statue.