193. A question about cubes. Professor Rackbrain one morning noticed that the cubes of consecutive numbers, starting from 1, can sum up to a perfect square. For example, the sum of the cubes of 1, 2, and 3 (i.e., \(1 + 8 + 27\)) is 36, or \(6^2\). The professor claimed that if taking consecutive numbers starting not from 1, the smallest numbers whose cubes sum to the square of some number are 23, 24, and 25 (\(23^3 + 24^3 + 25^3 = 204^2\)). Professor Rackbrain proposed finding the two smallest sets of consecutive numbers, starting not from 1 and consisting of more than three numbers, whose sum of cubes is also equal to the square of some natural number.
193. The cubes of all numbers from 14 to 25 inclusive (a total of 12) sum up to \(97344=312^{2}\). The next five cubes after the smallest answer are \(25,26,27,28\) and 29, the sum of which equals \(315^{2}\).