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The cube of any number, X is X*X*X
No. Not is x = 0 or if it an imaginary number.
No. And the proof is simple. Suppose there were such a number, X. Then X+1 is also a number and X+1 does not divide X.
x is a placeholder for a number. Depending what number you decide that x should be, it will be a prime number, or it won't.
If x is the given number and n is any whole number, then the question requires x = x*n which implies that x is zero.