How many total cubes do you have? The 32 cube door in that area is how you "beat the game", but that's really only the beginning anyway, so I'd go through that door as soon as you can (go back and collect some of the cubes you missed if you have to). When you beat it the first time, it unlocks New Game+, which carries over all your items and gives you a new ability that you need to get a lot of the anti-cubes. The map will show you which rooms still have items and secrets (if there's a gold outline you have everything, if it's white you don't and if there's a '?' it usually means there's still an anti-cube or something). The throne rooms have something written on the wall that you can only see with the added ability in New Game+ (the solution for that is actually kind of obtuse), and I think the owl effigy says something about "assembling the parliament" or some shit (there are 4 or so owls in the game you can talk to, and they'll fly off and congregate somewhere when you do).
