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There are only a handful of numbers in the range [1,100] that are perfect cubes of whole numbers.
These are:
The next highest would be 53, which is 125, greater than 100.
1, 8, 27, 64
There are 100 x 100 x 100 = 1 million cubic centimeters in a cubic meter. there are thus 100/1 million = 10-4 meters cubed in 100 centimeters cubed.
A number can't be cubed and prime. Cubed numbers (other than 1) have more than two factors.
1 million (100 cm = 1 m, 100 x 100 x 100 = 1 000 000)
1 metre cubed is 100 cm cubed so 1,000,000