No.
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It is the cube of a prime number.
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
37 is not a cube number but it is a prime number because it has only two factors which are itself and one
8 if 1 is included as a prime number or 27