Mathematical Induction Question About A Basis Step Use mathematical induction to show that:
$1^3 + 3^3 + 5^3 + ... + (2n + 1)^3 = (n+1)^2(2n^2+4n+1)$ whenever $n$ is a positive integer.
I am able to solve this problem, but the thing that confuses me on this is the Basis Step.
P(1): $(2(1) + 1)^3$ $\neq$ $4(7)$, does this mean that this problem can not be proved using mathematical induction, or am I missing something? Thanks.

Don't start at $n = 1$.  Start at $n=0$.
$P(n = 0): (1)^3  = (0 + 1)\left(2\times0^2 + 4*0 + 1\right) =1$
$P(1): 1 + 3^3 = 2^2\times\left(2 + 4 + 1\right)$
