Is $7$ the only prime followed by a cube? I discovered this site which claims that "$7$ is the only prime followed by a cube".  I find this statement rather surprising.  Is this true?  Where might I find a proof that shows this?

In my searching, I found this question, which is similar but the answers seem focused on squares next to cubes.

Any ideas?
This is certainly true. Suppose $n^3 - 1$ is prime, for some $n$. We get that $n^3-1 = (n-1)(n^2 + n + 1)$ and so we have that $n-1$ divides $n^3 - 1$. If $n-1&gt;1$ then we're done, as we have a contradiction to $n^3 - 1$ being prime.
Wouldn't $-2$ also be a prime followed by $-1$ which is a cube of $-1$.
As $x^2 + x +1$ will also equal one for $x=-2$.