Different ways of paining cube with 3 colors

Question

In how many different ways can a cube be painted by using three different colors of paint?

Answer 1

It is a harder question than 3^6 if you interpret it in the only interesting way possible: how many distinct (i.e. up to symmetry) ways are there to color a cube. Here's a paper: http://www.math.wayne.edu/~danf/talks/CF.pdf, and the answer is apparently 57.

Answer 2

Why? The answer is as always: 42

(ps. 3^6=729)