I don't know if this is programatically possible, but if it is, ChessCube should force gameplay to be executed only if the browser window is maximized. I entered a game and then windowed my browser with the game onscreen, I could manage to reduce the game to about 50% of the total screen, so that the rest remained showing my desktop. It's just a guess really, but I think windowed gameplay could favor cheating by allowing the bandit to use the remaining screen for bandit purposes, such as looking opening position moves lists, watching a cheating program or stuff like that.
That's just a thought, but it might be of help if programming that is possible.
Thanks for your attention.