For how many intergers n with |n| <500 can the polynomial Pn (x)=x6+n be written as a product of non-constant polynomisld with integer coefficients?

x^6 + n where n is an integer, can be factored into products of non-constant polynomials whenever n is a positive or negative perfect cube.....

Thus....... ±1,±8, ±27, ±64, ±125, ±216, ±343

So.....fourteen integers

Would you like to expand on this Chris?