Mike brought cake VS mike brought cake with him
'With him' may be used to emphasize 'at the moment'. E.g. 'Does he have his guitar?' May be interpreted more ambiguously than 'Does he have his guitar with him?'.
When using 'brought', the assumption that it is 'with him' is a pretty safe one to make, but occasionally people will automatically add the redundant 'with him' without realizing it's unnecessary.
It seems completely unnecessary because it is completely unnecessary. I don't think it could ever add anything useful except in the unlikely instance that there were other ways Mike could have brought his guitar and the speaker desperately needs to distinguish among them.
Listen, the thing is, people, like, often decorate their speech with, like, meaningless, er, decorations. Innit. Know what I mean?