First, write 8x^3 in exponential form (8 is basically the same as 2^3)
So that you have 2^3*x^3+1
Multiply the terms with equal exponents by multiply the bases (1 is basically the same as 1^3)
So that it becomes (2x)^3+1^3
Then, using a^3+b^3 equals (a+b)(a^2-2ab+b^2), factor the expression so that it becomes
(2x+1)((2x)^2-2x+1^2)
Expand the second bracket
So the two factors are (2x+1) and (4x^2-2x+1)