Beorn was human, we do know that. He could have inherited it but I think he learned it. Earlier in this thread a quote was posted that related to Radagast.
Quote:
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Radagast is, of course, a worthy Wizard, a master of shapes and changes of hue.
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Based on the way Beorn acted when Gandalf mentioned Radagast in The Hobbit, we can make the assumption that Beorn knew Radagast. I would quote but I do not have my copy of The Hobbit with me since I am on vacation. So we can make the assumption that Beorn possibly learned how to shape shift from Radagast.