Squares which are Difference between Two Cubes

Theorem

$169$ is the smallest square number which is the difference between two cubes:

$169 = 8^3 - 7^3$

Proof

 $\displaystyle 8^3 - 7^3$ $=$ $\displaystyle 512 - 343$ $\displaystyle$ $=$ $\displaystyle 169$ $\displaystyle$ $=$ $\displaystyle 13^2$