He served in the U.S. Army during the Korean War, where he played alongside jazz saxophonist Cannonball Adderley in the military band.

When Berry Gordy launched Motown Records in 1959 he recruited the Joe Hunter Band with Cosby, Benny Benjamin, James Jamerson, Larry Veeder, and Mike Terry, forming the basis of the ever-growing group of studio musicians contracted to the company.

These studio musicians became known as the Funk Brothers, and as a member of their early line-up Cosby performed on hundreds of Motown recordings in the 1960s, including Martha Reeves & the Vandellas US#2 hit "Dancing in the Street" (1964).

[4] In addition to his saxophone playing, Cosby showed Gordy his talents as an arranger, producer, and songwriter, and became a key collaborator with the young Stevie Wonder.

[6] Cosby died at age 73 on January 22, 2002, at the William Beaumont Hospital in Royal Oak, Michigan,[7] after complications from a cardiac bypass surgery.