Sure. You just can't fly AA.

I don't know where you're getting the MIA-HAV flight so it's hard to tell why it's there. LA used to run something like SCL-HAV-MIA-CUN-HAV-SCL or something equally as odd but I think they don't anymore. Regardless, you can't just book the HAV-MIA sector. AA has some charter flights but they aren't available to anyone but a very select group. They might be showing up because they have AA flight numbers but they are not bookable under any circumstances.

You can get a ticket from Cancun to Havana for about $200.