[tex]\text{Use}\ a^3-b^3=(a-b)(a^2+ab+b^2)\\\\27x^3-125=3^3x^3-5^3=(3x)^3-5^3=(3x-5)[(3x)^2+(3x)(5)+5^2]\\\\=\boxed{(3x-5)(9x^2+15x+25)}[/tex]
