He studied at Oxford University, the Art Students League (under George Bridgman), the Yale University School of Fine Art, and Princeton University Graduate School, where he received his Ph.D. Cooke is known more for his work in art history than for his painting, having written several texts, especially Painting Lessons from the Great Masters in 1967.
Part of his duties as curator included heading the Expert Opinions Section of the National Gallery, where owners of artworks could come and have their art appraised or otherwise identified.
Cooke's successes may have been more visible in art history, but he was also well regarded as an artist.
Not only was he appointed director of the American pavilion at the Venice Biannual International Art Exhibition, he was also named artist-in-residence at Princeton for four years and later won the Prix de Rome and a Fulbright Fellowship.
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