How do we find the formula for quadertic sequences?

A quadratic sequence is a series of terms that respect the
following:

1^2, 2^2, 3^2, 4^2, ......, n^2,
....

We'll consider n terms of the quadratic sequence and
we'll calculate their sum:

1^2 + 2^2 + 3^2 + ... + n^2 = S
(1)

We know that the formula for the squares of the first
terms of the sum is:

S =
n(n+1)(2n+1)/6

Now, we can have any number of terms of the
quadratic series, we'll also be able to determine their sum.