Simplify (2x)^3+2^3x

(2x)^3 + (2^x)^3

that's a sum of cubes, so
(2x + 2^x)((2x)^2 - (2x)(2^x) + (2^x)^2)
(2x + 2^x)(4x^2 + 2x*2^x + 2^2x)

I'm not sure that's any simpler.

Maybe you just wanted

8x^3 + 2^3x

?