Henry Ernest Dudeney/Puzzles and Curious Problems/122 - A Question of Cubes

Puzzles and Curious Problems by Henry Ernest Dudeney: $122$

A Question of Cubes

From Sum of Sequence of Cubes, the cubes of successive numbers, starting from $1$, sum to a square number.

Thus the cubes of $1$, $2$, $3$ (that is, $1$, $8$, $27$), add to $36$, which is the square of $6$.

If you are forbidden to use the $1$, the lowest answer is the cubes of $23$, $24$ and $25$, which together equal $204^2$.

What is the next lowest number, using more than three consecutive cubes and as many more as you like, but excluding $1$?

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Various Arithmetical and Algebraical Problems: $122$. -- A Question of Cubes
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $195$. A Question of Cubes