Hm, I thought I had a counterexample, but it looks like it was just a case of learning by imitation. Also, vervet monkeys teach their proto-language (of "eagles!", "snakes!", and "leopards!") to their young by smacking them when they give the wrong call.

As for other mammals, there are cases of them teaching each other when they learn something new, for example when an elephant learned how to unlock her cage.