Perfect Cubes

Fermat's Last Theorem states that when $a$, $b$, $c$ are non-zero integers and $n$ is a natural number greater than 2, there are no natural numbers $a$, $b$, $c$ satisfying $a^n = b^n + c^n$.

However, it is not hard to find natural numbers greater than 1 that satisfy the perfect-cube equation $a^3 = b^3 + c^3 + d^3$. For example, $12^3 = 6^3 + 8^3 + 10^3$.

Given an integer $N$, write a program that finds every quadruple ${a, b, c, d}$ satisfying this perfect-cube equation with $2 \le a \le N$. Here $b$, $c$, and $d$ are all greater than 1 and satisfy $b < c < d$.

The first line contains an integer $N$ ($2 \le N \le 100$).

Print each solution on its own line in increasing order of $a$; for the same $a$, order by increasing $b$, then $c$, then $d$. Each line has the form:

Cube = a, Triple = (b,c,d)

If no quadruple satisfies the conditions, print nothing.

Fermat's Last Theorem was proved by Andrew Wiles in 1995.