Thanks everybody.

It is quite difficult to get info on the web since most websites block Havana, must be a US thing. Air Jamaica refuses to price anything, claiming it is illegal in my country (Spain?). Lan Chile does not allow reservations (La Habana does not show up in the reservation page, only on the weekly timetable). Cayman Airways likewise does not allow to price it , only shows flight times.
I will just ask Iberia to issue it with the LA connection to CUN, and see what they say.