Here's how I would do it.
Cut out your squares as you normally would in the size you want them to be. Remember you'll be having many seams in the block itself, so you'll have to make it a big enough block.
Cut blocks out of different colors of fabric, all the same size.
Stack them and cut vertically and horizontially. Then take one of the cuts and move it to the bottom of the stack, take another cut and move it to the middle of the stack. Keep doing this until you have a different color in each of your blocks.
Then sew together all the cut you've made to form that block.
Then sew the blocks together.
I hope that makes sense..