Idiot is some dumb one, he admitted (8)
I believe the answer is:
bonehead
'idiot' is the definition.
(both can mean a stupid person)
'some dumb one he admitted' is the wordplay.
'some' says the answer is hidden in the clue (some of the parts of the word are used).
'BONEHEAD' can be found hidden inside 'dumb one he admitted'.
'is' is the link.
(Other definitions for bonehead that I've seen before include "Stupid person with ossified cranium" , "dope" , "Idiot" , "stupid leader" , "Fool" .)