Cambridge won a four-year scholarship to study medicine at Hofstra University but decided, instead, to become an actor, leaving college in his third year. He acted in many off-Broadway productions, winning the Village Voice's Obie Award in Jean Genet's "The Blacks"; and, on Broadway, he gained a Tony Award Nomination in "Purlie's Victorious". It was as a comedian that he broke into television, initially on The Tonight Show Starring Jack Paar (1957) (aka "The Jack Paar Show"). Having previously had occasional parts, he established himself in films in the late sixties. He played both comic and straight roles but is likely remembered for such portrayals as that of the white bigot who wakes up one morning to find himself turned black in Watermelon Man (1970). His compulsive eating probably contributed to his untimely death at 43 on the set of the television film Victory at Entebbe (1976), in which he was to have played General Idi Amin.