Numbers with both 3rd and 7th radical integers

Question

I was wondering if there are any Numbers where both the 3rd radical and the 7th radical are integers.

For example: 3rd radical of 125 is 5 (integer) 7th radical of 125 is 1.9932.. (no integer)

I didn't find any numbers where both radicals are integers. Do you have any ideas?

Answer 1

Check 21st powers, such as $1$ or $2097152$ or $10460353203$.