An unknown anime on cartoon network?

The one I think you are looking for is Tenchi Universe. Cartoon Networked played Tenchi Muyo, Tenchi in Tokyo and Tenchi Universe. The last two were spin offs of tenchi Muyo. Now as far as the word "prince" that word is used more in Tenchi Muyo and Tenchi universe. Though the big sword you will find in Tenchi in Tokyo. The reason you think they go together is because they basically had the same characters in all of the (few minor changes). But it played on CN and I am 99% sure this is the anime, or in this case, animes you are looking for.