It is the cube of a Prime number.
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All numbers have cube roots (not necessarily integral cube roots) so every prime has cube roots.
No.
The cube root of this number is 1 more than the smallest prime?
don't know if I understand your question, but: there are no numbers that are both cube numbers and prime numbers 8 is a factor of 16 that is a cube number (2^3) 2 is a factor of 16 that is a prime number
Yes. For example 3 is the cube of cuberoot(3). However, by definition, a prime number cannot be a PERFECT cube.