A perfect cubed number is anything that has the same 3 numbers multiplied. For example, 3*3*3= 27 so 27 is a perfectly cubed number.
If you had the number 54, you would look for factors of 54 that would have a perfect cubed number.
So factors of 54 are (1, 2, 3, 6, 9, 18, 27, 54)
So if you looked through the numbers, you would see that 27 is the perfect cubed number.
So, back to the question, go through the factors of 24 and see what number has 3 of the same numbers multiplied to get that number.