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Cubas grew up in a conservative family. Cubas wanted to become a priest, and he attended a Catholic seminar school with that purpose in mind, but he left the school after two years. He has admitted that later on as a teenager, he attempted to commit suicide.
Cubas started to become involved in the entertainment world when he met and made a friendship with members of Los Chamos, a famous 1980s boy band. Cubas led Carlos Baute to become involved in Los Chamos. Cubas also became a friend of Menudo's Ricky Martin. From 1984 to 1987, Cubas himself became a member of Los Chamos.
In 1987, Cubas made his telenovela debut, participating in Mi Amada Beatriz (My Beloved Beatriz), which was a successful telenovela in Venezuela and the rest of Latin America. Cubas participated in two other telenovelas before he joined Guillermo Dávila and Sonya Smith in 1992's Cara Sucia (Dirty Face), one of Venevision's most famous telenovelas of all time. He played "Antonio (Tony) Gonzalez", an ambitious man, in Cara Sucia, which gave him international celebrity. He shaved his head and has participated in seventeen other film productions since.
Cubas' sexuality has been questioned over the years, to which he responded on an interview that he "will never respond to anyone (about that)". Nevertheless, there have also been rumors about a romance with Venezuelan actress Mimi Lazo. Cubas has a daughter who was born in 1987.