What 3-digit number is a perfect square and a perfect cube?

##729=9^3=27^2##

The answer must be ##a^6## for some integer ##a## due to the properties of exponentiation. Only ##3^6 = 729## lies in the required range.

##3^6 = (3^2)^3 = 9^3##

##3^6 = (3^3)^2 = 27^2##