In SA BDM Indexes he is listed as being born on 24/8/1847 along with his brother William - that would make them twins.
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This biography is a rough draft and needs to be edited and primary sources included
Sources
South Australia Birth Index. (Genealogy SA, https://www.genealogysa.org.au/index.php : accessed 22 Aug 2022) database entry for William COX (Birth date 24 Aug 1847, Father William COX, Mother Eliza HOBART, Birth residence Adelaide) Reference: District Adelaide, Book/Page 2/14. Notes: Symbol M (Identifies multiple births).
South Australia Marriage Index. (Genealogy SA, https://www.genealogysa.org.au/index.php : accessed 22 Aug 2022) database entry for William COX (age 28, marital status S, father William COX) and Florence KEKEWICH (age 19, marital status S, father Henry George KEKEWICH) 19 Jul 1876, Wesleyan Parsonage Mount Gambier. Reference: District Grey, Book/Page 108/194.
South Australia Death Index. (Genealogy SA, https://www.genealogysa.org.au/index.php : accessed 22 Aug 2022) database entry for William COX (Death date 9 Nov 1930, age 83, marital status M, place of death Mount Schank, residence Mount Schank) Reference: District Grey, Book/Page 524/536.
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DNA Connections
It may be possible to confirm family relationships with William by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
However, there are no known yDNA or mtDNA test-takers in his direct paternal or maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with William: