Factor completely. 8x^3-27. show solution with explanation.

Here we are given 
8x^3-27
now making both as a cube root
(2x)^3-(3)^3 
using formula cube root
 a^3-b^3=(a-b)(a^2+ab+b^2)
where 
a=2x
b=3
now putting these values 
2x^3-3^3=(2x-3)(2x^2+2x*3+3^2)
simplifying
2x^3-3^3=(2x-3)(4x^2+6x+9)
hence the right answer is 
2x^3-3^3=(2x-3)(4x^2+6x+9)