The Joe Cuba Sextet The Legendary Iconic Sextet uses a mixture of Spanish and English lyrics.

In 1962, after recording three albums for Mardi Gras Records, Cuba recorded his first album with the Joe Cuba Sextet called Steppin' Out featuring the hit "To Be With You", featuring the vocals of Cheo Feliciano and Jimmy Sabater Sr. The band became popular in the New York Latin community. The lyrics to Cuba's music used a mixture of Spanish and English, becoming an important part of the Nuyorican Movement.

In 1965, the Sextet got their first crossover hit with the Latin and soul fusion of "El Pito (I'll Never Go Back to Georgia)". The "I'll Never Go Back to Georgia" chant was taken from Dizzy Gillespie's intro to the seminal Afro-Cuban tune "Manteca." Sabater later revealed that "None of us had ever been to Georgia."

Along with fellow Nuyorican artists such as Ray Barretto and Richie Ray, Cuba was at the forefront of the developing Latin soul sound in New York, merging American R&B styles with Afro-Cuban instrumentation. Cuba was one of the key architects behind the emerging Latin boogaloo sound, which became a popular and influential Latin style in the latter half of the 1960s. In 1966, his band scored a hit on the United States Billboard Hot 100 with the song "Bang! Bang!". The record peaked at No. 63 on the Hot 100, and No. 21 on the R&B chart.

Willie Villegas long time member of The Joe Cuba Sextet continues the legacy of this dynamic and versatile sextet after Joe's passing.