"He just ate the cake." has two possible meanings. 1. His has just finished eating the cake. 2. He ate only the cake and nothing else. "He has just eaten the cake." also has the same two meanings, but with a different tense. However, the interpretation most people would make is that he has just finished eating the cake. The interpretation is more certain. However, "He have just..." is incorrect. It should be "He has just..." Both tenses can be used with no error. The second has a slightly clearer meaning.