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

by : $122$

 * 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 $1$?