The Cuban-Mexican War began in Grand Theft Auto: Vice City Stories. It was a turf war between the Cubans and the Cholos. It started in 1984 when the Cubans arrived in Little Havana. This got the Cholos angry, causing a turf war between the two opposing gangs. Later, to rile the Cubans, they caused chaos in Little Havana, which lead up to the mission Papi Don't Screech when the Cholos threaten to kill Umberto Robinas father.
Vic has to fight his way into the warehouse and defend the two vans packing the heat. But after they take the guns and go, Vic plants bombs in the Cholo's pinata. This pinata bomb kills many Cholos. Because of this Little Haiti becomes a gang-free community for a while.
GTA Vice City
Sometime between 1984 and 1986, the Haitian Gang takes over Little Haiti again. This eventually leads to another gang war. Later on, Tommy Vercetti frames the Cubans for killing a Haitian gang lord, which sparks another turf war in both gangs' respective communities.