Good question, but define "communist".

They had Castro as a leader for a long time, in a basic dictatorship. That's pretty communist.

They also have had free public health care, and a super-tight trade embargo, which is why they all drive cars from the 1950s.

Apparently the quality of life is fairly high, and the people are friendly. But it's not exactly a wealthy place by any means.

Under the national constitution, Cuba is a socialist democracy, with the Communist Party of Cuba as the "leading force of society and of the state", although elections are nominally non-partisan.

https://en.wikipedia.org/wiki/Elections_in_Cuba

So they're run by a party called "The Communist Party of Cuba". That's pretty communist.

But then there's this:

In 2011, "The new economic reforms were introduced, effectively creating a new economic system, referred by some as the "New Cuban Economy". Since then, over 400,000 Cubans have signed up to be entrepreneurs. As of 2012, the government lists 181 official jobs no longer under their control—such as taxi driver, construction worker and shopkeeper.

So it's not super-duper communist. Just mostly communist, I guess? Kind of like China, they're becoming more interested in free trade, but at the same time the Communist party maintains a complete stranglehold over the governmental system and has for decades.

https://en.wikipedia.org/wiki/Economy_of_Cuba#Post-Fidel_reforms