Henry Ernest Dudeney/Modern Puzzles/94 - Adding their Cubes

Modern Puzzles by Henry Ernest Dudeney: $94$

Adding their Cubes

The numbers $407$ and $370$ have this peculiarity, that they exactly equal the sum of the cubes of their digits.

Thus the cube of $4$ is $64$, the cube of $0$ is $0$, and the cube of $7$ is $343$.

Add together $64$, $0$ and $343$, and you get $407$.

Again, the cube of $3$ ($27$), added to the cube of $7$ ($343$), is $370$.

Can you find a number not containing a nought that will work in the same way?

Of course, we bar the absurd case of $1$.

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Arithmetical and Algebraical Problems: Various Arithmetical and Algebraical Problems: $94$. -- Adding their Cubes
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $143$. Adding their Cubes