Cox grew up in Cambridge, Massachusetts. In 1920, while still a high school student, he studied with Charles Hawthorne in Provincetown, Massachusetts. In 1923 he entered Harvard College, but left at the end of his third year, having won the Harvard Lampoon art award for travel. From 1928 to 1930 he was a student at the Museum of Fine Arts School, Boston, and attended the architectural school of the Massachusetts Institute of Technology, Cambridge, 1929-31. Initially he practiced architecture in his father's Boston firm, Putnam and Cox, but in 1936 he turned to painting as a full-time pursuit. Within three years he had begun to exhibit his portraits.
Although Cox painted a wide variety of subjects, he enjoyed an especially successful career as a portraitest. Among his many celebrated sitters were Robert Frost, Robert F. Kennedy, and several justices of the United States Supreme Court.
Cox was a member of the National Institute of Arts and Letters, and served on the Massachusetts Art Commission, and as a trustee of the American Academy in Rome.
