Factorize $8a^3 + 27b^3$:

This is a sum of cubes $(2a)^3 + (3b)^3$, which factors as $a^3+b^3 = (a+b)(a^2-ab+b^2)$. With $a=2a,\ b=3b$ this gives $(2a+3b)(4a^2-6ab+9b^2)$; note the middle term is $-6ab$, not $+6ab$.