When were capes invented?

You may have better luck taking this question to /r/AskAnthropology - capes and mantles can be found in all or most ancient societies. Essentially, they are unshaped lengths of fabric that can be pinned or tied into place, so they most likely came about in a number of places independently.

What have they represented since their invention?

Can you please rephrase this part of the question? I'm not sure I understand what you're looking for.