We know that the number 7 is the prime followed by a cube. Which next number is also a prime followed by a cube ?

There is no number other than 7 that is a prime followed by a cube.

To prove, let us assume that n3-1 is a prime for n.

N2-1 = (nâˆ’1)(n2+n+1)

Now, n-1 divides n3-1.

If n-1>1, then we are done as it is a contradiction to n3-1 being a prime.