Find all primes of the form $n^3-1,n\in\mathbb N,n>1$

Question

First prime is $p_1=7$ is for $n=2$.

Checking $n=\{3,...,10\}$ gives no primes.

How to evaluate primality in this case ($n^3-1$) and in general case (mathematical solution)?

Answer 1

Hint: Note that $$ n^3 - 1 = (n-1)(n^2 + n + 1) $$ When can this be a prime?