119. Extracting Roots. Once, in a conversation with Professor Simon Greathead, a man of rather eccentric mind, I mentioned the extraction of cube roots.

- Amazing, - said the professor, - what ignorance people show in such a simple matter! It seems that in the extraction of roots, since the only roots were those extracted with a spade, fork, and garden trowel, the world has not advanced at all. For example, no one except me has yet discovered that to extract the cube root of any number, it is enough to find the sum of its digits.

Anyone can extract the cube root of 1. Although this example supports my statement, it is too trivial and we will not consider it. Suppose we need to extract the cube root of 512. We find the sum of the digits, which is 8, and the answer is obtained!

I suggested that we might be dealing with an exceptional case here.

- Not at all, - the professor objected, - let's take another number at random, say 4913. The sum of its digits is 17, and 17 cubed equals 4913.

I did not dare to contradict the scholar, but I ask the readers to find all other numbers whose cube root coincides with the sum of their digits. There are so few of these numbers that they can literally be counted on the fingers.
119. The sought numbers are 5832, 17576, and 19683. The sum of the digits of each of them, equal to 18, 26, and 27, respectively, coincides with the corresponding cubic root.