Question

Factoring
8x^3 + 125 = 0

Answer 1

supposedly it might be the quadratic formula

Answer 2

Quadratic formula does not work because this is not a quadratic equation (highest power is 3 which makes it cubic)

Nonetheless, it is a sum of cubes, so you can use

a^3 + b^3 = (a + b) (a^2 - ab + b^2)

letting a^3 = 8x^3, that makes a = 2x
and if b^3 = 125, that means b = 5

so plugging in a and b where appropriate:

8x^3 + 125 = (2x + 5) (4x^2 - 10x + 25)

the quadratic part from this doesn't have any real roots, so as long as it doesn't ask for imaginary roots, you can stop here