Cocker worked very skillfully as an engraver and is mentioned favourably in Samuel Pepys' Diary. His other works include several writing manuals, poems for transcription or translation, and an English dictionary. In 1657 Cocker was living in London, where he also taught writing and arithmetic. The Arithmetic was edited and published in 1678 and passed through more than 100 editions. A 19th-century writer declared the editor of the 1678 edition, John Hawkins, to have been the author, rather than Cocker.