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

by : $123$

 * Two Cubes
 * Can you find two cube numbers in integers whose difference shall be a square number?
 * Thus the cube of $3$ is $27$, and the cube of $2$ is $8$,
 * but the difference, $19$, is not here a square number.
 * What is the smallest possible case?