Henry Ernest Dudeney/Puzzles and Curious Problems/86 - Digits and Cubes

by : $86$

 * Digits and Cubes
 * ''Find all $5$-digit squares such that:
 * the number formed from the first $2$ digits added to that formed by the last $2$ digits form a cube.


 * For example, $141^2 = 19 \, 881$, where $19 + 81 = 100$.
 * But $100$ is a square not a cube.


 * How many are there altogether?