A perfect cube is a number whose cuber root is a whole number. When we find the cube root of 21500 we get the following.

\begin{aligned} 

&\sqrt[3]{21500}=27.806

\end{aligned}

As we can see the cube root of 21500 is not a whole number, which means it is not a perfect cube. 

As a rule of thumb, if a number has less than three zeros in the ones, tens and hundreds place, it is not a perfect cube. 21500 has only two zeros. Hence, not a perfect cube. 

Examples of perfect cubes can be 1000, 8000, 27000 etc.