How many ways can six 8-peg lego blocks of six different colors be combined? I have seen the number quoted as > 650 billion. The quote is from a Danish mathematician, Soren Ehlers. Intuitively, this does not seem correct to me. Any mathematicians/statisticians out there who can help either verify the huge number, or give me a correct number?
To expand on Zhaph's answer, I'm assuming that you have a fixed set of six colors, and each block is one color.

If that's the case, this is a simple combination problem on top of the orientation problem.  Since there are six colors and six bricks, there are 6! ways to assign those six colors to the six bricks, or 720 ways.

Now, we apply this combination to our orientation, and get:


  915,103,765 orientations x 720 color combination/orientation = 658,874,710,800 combinations