The Cuban vote has been Republican. Only recently has it started to sour. Witness Obama winning FL-26 (which elected a rat over a scandal-plagued Republican) and FL-27 in 2012 whereas he lost them in 2008. He got over 60% in Miami-Dade, better than his showing in Palm Beach County!
Gore in 2000 got only 52.5% in Miami-Dade. I’m sure Bush won the Cuban vote that year also. Gore was trolling for Black votes in the recount.
I believe that the 2000 exit polls in FL gave Bush 83% of the Cuban vote, with high turnout. It was right after Clinton ordered Eián to be captured at gunpoint on Easter Sunday and sent him back to Castro’s Cuba; FL Cubans had flirted with voting for Clinton in 1996 after he signed Helms-Burton into law, giving Dole a relatively small majority.
The 2012 results were shocking, with Romney winning a slim majority of the Cuban vote in FL. That whole “immigration reform” bullshiite was seen as the culprit, which I believe is why Rubio has embarrassed himself pushing “reform.”