Henry Ernest Dudeney/Modern Puzzles/95 - Squares and Cubes

Modern Puzzles by Henry Ernest Dudeney: $95$

Squares and Cubes

Can you find two whole numbers, such that the difference of their squares is a cube and the difference of their cubes is a square?

What is the answer in the smallest possible numbers?

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Arithmetical and Algebraical Problems: Various Arithmetical and Algebraical Problems: $95$. -- Squares and Cubes
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $177$. Squares and Cubes