A number theory problem by Kaleem Kħặŋ

Being both a perfect square and a perfect cube means that it is a perfect 6th-power.
$1^6=1$
$2^6=64$
$3^6=729$
The answer is 64.

Consider this: We need a two digit number which is a perfect square and perfect cube. Therefore, its power must include 2 & 3. Now multiply 2 &3 getting 6. We will have this (6) as the power of 2 because we want a two digit number. Hence, 2^6 = 64.