Given any two polynomials in a single variable it is always possible to eliminate the variable and obtain a formula showing the relationship between the two polynomials.

${\displaystyle \begin{array}{ccc}\multicolumn{1}{c}{a(n)}& =& 1+2+3+...+n\\ \multicolumn{1}{c}{b(n)}& =& 1^2+2^2+3^2+...+n^2\\ \multicolumn{1}{c}{c(n)}& =& 1^3+2^3+3^3+...?+n^3.\end{array}}$

It is well known that c = a ². What are the relationships between a and b and between b and c?