Cambridge won a four-year scholarship to study medicine 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 "Tonight 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) (TV), in which he was to have played General Idi Amin .

Died of heart attack on set of TV movie Victory at Entebbe (1976) (TV), where he was set to play Ugandan dictator Idi Amin . Amin claimed Cambridge's death was "punishment from God."Biography in: "Who's Who in Comedy" by Ronald L. Smith. Pg. 86-87. New York: Facts on File, 1992. ISBN 0816023387Was nominated for Broadway's 1962 Tony Award for Best Supporting or Featured Actor (Dramatic) for "Purlie Victorious," a role he recreated in the film version titled Gone Are the Days! (1963).Was originally set to star in "The Partners" (1971) but left during filming of the pilot because he did not get along with Don Adams .