Are There Any 3 Digit Numbers That Are Both Perfect Cubes And Perfect Squares? If So What Are Their Interest Ratings?

729 = 3⁶ = (3²)³ = (3³)²
_____
The "interest rating" is apparently computed from a weighting of several features of the number.
15(prime)+10(cube)+7(square)+4(∑digits >14)+3(even)+2(odd)+(#factors).

Obviously this odd square/cube is not prime. The sum of the digits is 18, and it has 7 factors.
Interest Rating = 10+7+4+2+7 = 30.