Henry Ernest Dudeney/Puzzles and Curious Problems/124 - Cube Differences

by : $124$

 * Cube Differences
 * If we wanted to find a way of making the number $1 \, 234 \, 567$ the difference between two squares,
 * we could of course write down $517 \, 284$ and $617 \, 283$ --
 * a half of the number plus $\tfrac 1 2$ and minus $\tfrac 1 2$ respectively to be squared.


 * But it will be found a little more difficult to discover two cubes the difference of which is $1 \, 234 \, 567$.