Actually, no they are not. They drilled a bit with very little success.
Zarubezhneft abandons offshore drilling in Cuba, for now
http://www.cubastandard.com/2013/05/31/zarubezhneft-abandons-offshore-drilling-in-cuba-for-now-2/
May 31st, 2013
More than one month after the owner of a drilling platform said it would pull its rig from Cuba, state oil company Unión CubaPetróleo (Cupet) announced in a terse official note that Russia’s OAO Zarubezhneft postponed further offshore exploration.
The pullout effectively ends all offshore exploratory drilling in Cuba, for now. The failure by the Songa Mercur shallow-water rig to find oil in Block L, off Cayo Santa María in north-central Cuba, comes after four dry holes drilled by a deep-water platform in Cuban waters of the Gulf of Mexico in 2012. The lack of success, after five foreign oil consortia invested hundreds of millions of dollars in Cuba over the past couple of years, is dashing hopes to resurrect the cash-starved Cuban economy with oil.