Highest rates of population growth, shown above in dark green, are in the provinces of Santiago de Cuba and Guantanamo.
The population of Cuba was 5,876,052 in 1950. It had nearly doubled to 11,243,836 in 2005. Then it began dropping, showing declines in 2006, 2007 and 2008.
In 2009, the population rose slightly, but it is projected to fall again this year, Cuban government statistics show. (Source: page 3 of this 26-page document, in Spanish, which I spotted on the Cubapolidata blog).
The population is expected to continue to drop for at least the next 20 years and will fall below 11 million by 2032 "because of aging and a drop in the fertility rate," the Herald Tribune reported.
The number of Cubans leaving the island also has an impact on the trend, but the population document does not address that question.