If you have ever been in a boxing match, got paid for it, and can get a record authority to list your fight; you are/have been a professional boxer. It would probably next to impossible to get any kind of demographic break down.
You could always sort through the all time rankings on Boxrec but set the criteria to only Cuban boxers.
If Cuba was an open country, they'd dominate professional boxing, too, in all weights. Like they do in baseball.