Joseph Cubey was born in South Shields, the son of Thomas and Elizabeth Cubey. His father was a commercial traveller and biscuit manufacturer.

Joseph joined Westoe Secondary School from Westoe Juniors in 1896, and left to become an articled to South Shields architect, James Walter Hanson until 1905, after which he remained as an assistant in the practice until moving to be assistant to John Hill in Newcastle, and then to a position with Tynemouth-based architect, Arthur Plummer.

He attended Armstrong College, and qualified as an architect in 1907 following which he was admitted as an associate with the Royal Institute of Brtitish Architects. After this he joined the Land Valuation Office in Newcastle.

Joseph joined the 23rd battalion (4th Tyneside Scottish) of the Northumberland Fusiliers and was appointed Temporary Second Lieutenant in December 1914.

He was later promoted to Temporary Captain and, whilst on active service on the first day of teh Battle of the Somme, he was killed in action.

He was buried in the Ovillers Military Cemetery, in the north of France just outside of Albert.