How many whole numbers are there, whose squares and cubes have the same number of digits?

there are only 4 whole numbers whose squares and cubes have the same number of digits.

Explanations:

let 0, 1, 2 and 4∈W (where W is a whole number), then

, ,

, ,

, ,

, .

You can see from the above that only four whole numbers are there whose squares and cubes have the same number of digits