The first could be used if you have one or more brothers. The second can be used only if you have more than one. It gives the impression that you have several brothers.
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AlpheccaStars He is my brother. I use this 99.99 % of the time. He is a brother of mine. I only use this in the negative: He is no brother of mine.Thanks. I'd never have thought of that.
martinleeThe first example also means 'several brothers'Not necessarily. I can say 'He/this is my brother' if I have only one brother.
AnonymousThe first case is definite and the second indefeniteWhat do you mean by definite and indefinite?