The process of adding rational functions (ratios of polynomials) by placing them over a common denominator is the analogue of adding rational numbers. The reverse process of taking a rational function apart by writing it as a sum of simpler rational functions is useful in several areas of mathematics; for example, it arises in calculus when we need to integrate a rational function and in discrete mathematics when we use generating functions to solve recurrence relations. The decomposition of a rational function as a sum of partial fractions leads to a system of linear equations. Find the partial fraction decomposition of the given form.

Assume that 1² + 2² +........+ n² = an³ + bn² + cn + d. Find a, b, c, and d. [It is legitimate to use n = 0. What is the left-hand side in that case?]