One factor of 8x^3+1 is 2x+1 The other factor is?

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)