Madory wrote that there is no evidence of a submarine cable in use in Cuba in 2012. He said that latencies to Cuba are very stable and clearly satellite (>480 ms). He attached the following visualizations (click to enlarge):
The numbers in the figure legends indicate the connecting autonomous networks -- CubaData (11960) is the state telecom of Cuba, and they have three satellite providers Tata (6453), Intelsat (22351) and NewCom (32034).
Renesys is "The Internet Intelligence Authority" -- they constantly monitor the state of the global Internet. You may have seen their reports of network outages when nations went off line during the Arab Spring, for example, this Syrian episode. You can get a sense of what they do by following their blog and Internet events bulletin.