Name of “Charles Cox”, date and place of birth, died in infancy, added here in April 2022, and from a post written by Brian Brandon about 'James George Cox' on "The First Four Ships" website:
http://www.firstfourships.co.nz/pics/othrppl.php?table=others&id=56
Brian Brandon is a x2 great-grandson of James George Cox, and being descendant through James' son, James George Coleridge Cox.
Brian of nzolivers is also a x2 great-grandson of James George Cox, but descendant through James' daughter Elizabeth Annie Cox.

New given name of “Theodore” from search on New Zealand BDM website in April 2022:
1858/5786. Cox, Theodore Charles. Mother: Louisa. Father: James George

Full date of birth of 24 October 1858 confirmed from further searching in April 2022 on BDM Search by incrementally changing the date range for the birth.

Year and country of death, from death search on New Zealand BDM website in April 2022:
1859/2192. Cox, Charles Theodore. Died age 8M

Full date of death of 16 June 1859 from further searching in April 2022 on BDM Search by incrementally changing the date range for the death.