Twice a square

Find a positive integer NN such that p3+N2p^3 + N^2 is a perfect square for 2 distinct (positive) primes pp.

Details and assumptions

You may use a theorem of Ljunggren, which states that the equation x2+x+1=y3x^2+x+1=y^3 has only the following integer solutions: (x,y)=(0,1),(1,1),(18,7),(19,7)(x,y)=(0,1), (-1,1), (18,7), (-19,7).

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