31 Notice that the total so far is always 1 less than the number of grains that will be put in the next square. This pattern is true for any number of squares. You might want to investigate this to see why it is true. If this doesn't make sense to you, don't worry about it, but look for other ways to think about the pattern. Subtract 1 from this number, and you have the total number of grains on the first 64 squares.
Powers follow patterns or rules, too.
If you haven't seen this, I'll show you why it works. The multiplications get a lot bigger, but if you know how to estimate the size of a product, you don't need to do all the work to get a good idea of how big the total is. I've gone over a lot of ideas quickly. I don't know how many of these ideas you may already be familiar with.