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

by : $122$

 * A Question of Cubes

Solution

 * $\ds \sum_{n \mathop = 14}^{25} n^3 = 14^3 + 15^3 + 16^3 + \cdots + 25^3 = 97 \, 344 = 312^2$

The next one after that is:


 * $\ds \sum_{n \mathop = 25}^{29} n^3 = 25^3 + 26^3 + 27^3 + 28^3 + 29^3 = 99 \, 225 = 315^2$