Henry Ernest Dudeney/Puzzles and Curious Problems/123 - Two Cubes/Solution

by : $123$

 * Two Cubes

Solution
The answer given by is:
 * $8^3 - 7^3 = 512 - 343 = 169 = 13^2$

but it can be noticed that:
 * $2^3 - \paren {-2}^3 = 8 - \paren {-8} = 16 = 4^2$

which, because $8$ and $-8$ are both integers, is also a valid solution.