Is (CH3)3 a nucleophile or electrophile? And why?

Dear Student,
(CH₃)₃C⁺  is a positively charged electrophile. This is a tertiary carbocation which has an electrophilic centre (C⁺) is stabilized  +I effect of the 3 methyl groups  There is a deficiency of electrons at the carbon centre and hence it will behave as a electrophile. This is formed when when the leaving group is more electronegative compared to carbon or in the presence of an acid 
$(C{H}_3{)}_{3}C-Br \to ( C{H}_3{)}_3{C}^{+} + B{r}^{-}$ (Br more elctronegative compared to C)
(CH₃)₃C^- can also be formed when the leaving group is less electronegative or in the precence of a base . (CH_​3)₃C^- will be weak nucleophile because it has e^- rich C centre. It will be weak due to the destabilization of 3 methyl groups.
$(C{H}_3{)}_{3}C-H + base\to (C{H}_3{)}_3{C}^{-}+ H^{+}$ ( base will abstract the proton).
 The behaviour of (CH₃)₃C will depend on the path from which it is formed.
Regards!