sequences and series - Derive a polynomials formula by setting $n = 1$, $n = 2$, $n = 3$ to determine the coefficients.

Derive a formula for the sum of squares $1^2 + 2^2 + 3^2 + … + n^2$.

Hint: assume the formula is a polynomial of degree 3, i.e. $an^3 + bn^2 + cn + d$, and use the cases of $n=0, n=1, n=2$, and $n=3$ to determine its coefficients.