Lower, Mark A (1860) Patronymica Britannica: a dictionary of the family names of the United Kingdom. London: J.R. Smith. Public Domain.
COXE
As described in historical dictionaries
Patronymica Britannica (1860)
COX. COXE. See Eng. Surn. under Cock, i. 165. Probably a sjaionym of Little. It may, however, be the same as Cook, from its latinized form, thus : Cocus, Cocks, Cox.