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

Puzzles and Curious Problems by Henry Ernest Dudeney: $123$

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?

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Various Arithmetical and Algebraical Problems: $123$. -- Two Cubes
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $196$. Two Cubes