If you do a parent search on the IGI you will find a number of entries with those parents - I have listed a couple below but no James
Extracted IGI recordHENRY FREDERICH COMPTON CAVENDISH
Father: GEORGE AUGUSTUS HENRY
EARL OF BURLINGTON CAVENDISH Mother: ELIZABETH COMPTON
Marriages - FRANCES SUSAN LAMBTON Marriage: 15 JUN 1819 Saint James, Westminster
Submitted IGI records Charles Compton Cavendish Birth: 28 AUG 1793 of Chesham, Buckingham Death: 10 NOV 1863
Father: George Augustus Henry Cavendish
Mother: Elizabeth Compton
Marriages Catherine Susan Gordon 18 JUN 1814
George Henry Compton Cavendish Birth: 14 OCT 1784 Hardwick, Derby
Death: 22 JAN 1809 Father: George Augustus Henry Cavendish
Mother: Elizabeth Compton
PARENT SEARCH ON IGI
www.familysearch.org - On home page - click on “Advanced Search” to the right of the SEARCH button
Select “International Genealogical Index” from the left hand menu
Input fathers name and surname BUT only put mothers christian name as not all entries have the maiden name
REGION – select British Isles from the menu
COUNTRY – select one or “All countries”
COUNTY (will appear when you select COUNTRY) – leave as all counties
Click SEARCH