I don't have a too but my severe macaw has two play stands and walk in cage to sleep and play in when we r not home..I have a pix in my profile..I think it's 6'x6'x6' feet not inches'. We converted a dog kennel into a bird cage
U2-Poppy(Poppy lives with her new mommy, Misty now) CAG-Jack, YNA, Bingo, Budgie-Piper, Cockatiel-Sweet Pea Quakers-Harry, Sammy, Wilson ***Zeke (quaker) Twinkle (budgie) forever in our hearts
I'm not home where I could measure, but Rocky's "castle" (befitting The King of the Toos, as we call him) is as tall as I am, taller if you count the play top, and I'm 5'9". It's almost as wide. It takes a king size sheet for a cover and that doesn't cover it all, but he likes that because he wants to peer under the edge and talk to us after he's supposed to be in bed. They always say bigger is better.
My bare eyed is in a 40 by 30. Any bigger and he would have a heart attack from the open space and the ability for random dust balls to eat him while in that open space.
Whatever size cage you use for your cockatoo, please make sure he has plenty of out-of-cage time. If you could see them in the wild, soaring and swirling high in the sky, you'd realise how very much they need to exercise their wings. An outdoor aviary is such a good idea for cockies, but if you can't do that, then encourage him to fly indoors.
Sadly, here in Australia, lots of people keep cockatoos in a cage that's barely large enough for them to extend their wings. It's a horrible, cruel practice and I hope it will eventually die out.
Mine each have there own 80 x 40 & they use every inch of it, funny thing is there cages are a mirror of one another (same perches/toys, even the position of everything is the same) and they sit right across from each other, when they are out that run across the floor & climb on the others cage and check it out. I think they finally realized, hey this cage looks exactly like mine.