How do we guess some equations like 1^2 + 2^2 + 3^2 + ... + n^2 = [n(n + 1)(2n + 1)]/6 before we prove it?

How do we guess some equations like
1^2 + 2^2 + 3^2 + ... + n^2 is equal to [n(n + 1)(2n + 1)]/6
and
1 x 3 + 3 x 5 + 5 x 7 + ... + (2n - 1)(2n + 1) is equal to [(2n - 1)(2n + 1)(2n + 3) + 3]/6
before we prove it? Is it by trial and error?