Cucchiara debuted in the late 1950s, mainly recording cover versions of American hits, before starting his career as singer-songwriter in 1962. His first hit was the song " Annalisa", named after Cucchiara's first daughter. This song was used as closing theme of the RAI variety show Alta pressione. In 1970 Cucchiara debuted as a playwright with a musical titled Cassandra 2000. In 1972 he reached a large national and international audience, and critical success, with a musical comedy titled Caino e Abele ("Cain and Abel"). In later years Cucchiara focused his activity on stage, as author of other successful plays such as Pipino il Breve (1978) and La baronessa di Carini (1980). He also worked as television writer.