I believe the last Cubana IL62 operated in 2008. Cubana never operated the IL86. A lot of Cubana flights are operated by 767s and A320s which they charter in from various operators in Europe and Latin America. The notional types shown in their schedules are often well removed from reality.
The IL96 is their mainstream type, but they suffer from a range of issues with availability of spares and similar causes of the aircraft ending up AOG for periods of time. A shame, as the IL96 is a nice, modern feeling aircraft.