And the number of bricks in Hyrule Castle is....

424.

If you think I'm wrong, count them yourself!  I had to pause the game over 300 times to get all the angles necessary for the calculations, and there was some estimation involved with the depth of the castle (you never get to see the back side...) but I'm fairly confident of my approximation.  The hardest part was finding how tall the castle was; to do that, I had to pause the game repeatedly as I fell to my death on both sides.  As to the age-old debate of whether to count the "green" bricks: NO.  Those are not part of the Hyrule establishment itself, and furthermore a lot of those bricks seem to exist only in two dimensions.  Also, the spires seem to be composed of partial bricks, which don't count.  I also didn't count the bricks on the steps because those steps are pointless and serve no obvious structural purpose to the castle.  So the number I came up with was only grey bricks.

But feel free to come up with your own estimation!  It really is quite fun once you get the hang of it.  Now I think I'm going to go try out this so-called "fucking myself."  An overwhelming majority of you recommended it to me, and I've been researching the correct technique and I'm now ready to put it into action!  Wish me luck!