Cocks was born at Wild Duck Creek, near Heathcote, Victoria and educated at a state school at Richmond before entering retailing at 14. He married Elizabeth Agnes Gibb in 1884 and they had a son and a daughter. He established a business of wholesale jewellers and opticians, Arthur Cocks & Co. He was a member of the Sydney Municipal Council from 1906 to 1914 and was Lord Mayor in 1913.
Cocks represented St Leonards from 1910 to 1920 and St Leonards from 1920 to 1925, initially for the Commonwealth Liberal Party and then the Nationalist Party. He was Colonial Treasurer from 1922 to 1925 in the Fuller ministry.
Cocks was appointed a Knight Commander of the Order of the British Empire (KBE) in 1925.