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

Puzzles and Curious Problems by Henry Ernest Dudeney: $86$

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?

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $86$. -- Digits and Cubes
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $123$. Digits and Cubes