Prime cube partnership

There are some prime values, p, for which there exists a positive integer, n, such that the expression n³ + n²p is a perfect cube.

For example, when p = 19, 8³ + 8²×19 = 12³.

What is perhaps most surprising is that for each prime with this property the value of n is unique, and there are only four such primes below one-hundred.

How many primes below one million have this remarkable property?

Written by gamwe6 who lives and works in San Francisco building useful things. You should follow him on Twitter