I thought Cuba was a no flight zone for American airlines ! flightaware.com/live/flight/AAL1608
If you look at the details of the flight, you will see that location is approximate, ie a guesstamate for part of the fligtht. Take a look at the FAQ for flight data in areas that Flightaware does not have coverage.
I have flown from Miami to Managua a couple times on American Airlines and we flew over Cuba.