When can you start calling your boyfriend by a cute nickname?

You can do it whenever you like. Just do it gradually and every once in a while slip a "babe" or whatever into the conversation. Don't discuss it with him or plan it, because it makes it too forced and awkward. Guys like nicknames, just not in front of their friends, so keep that in mind. Try it out and if it's bad, you'll know! Best of luck :)