sun's volume in hard drives.

Even that might not be enough lol. There are more possible moves than there are atoms in the universe. If you get rid of what are likely illegal moves, it's (as you say) around 10^50. The space needed to even compute that, however, would be larger than our entire galaxy even with the most efficient computer possible that doesn't exist.

Go has over 10^170 moves, which is even more of a challenge to compute.