James would have been born before the start of civil registration (July 1837) - you need to get parish registers (I think) to get details of him.
And there are 13 James Fuller's in Sussex in 1841!
So it's probably best to get the marriage certificate, as that will have ages, addresses and father's names.
Marriages March qtr 1846 Lewes Vol 7, page 515
FULLER, James
WASHER, Lucy
There are 20 births registered in Lewes with a surname FULLER between 1845 and 1851.
It is not possible (using FreeBMD) to determine whose are Lucy & James children.