Answer
$(3x-2)(9x^2+6x+4)$
Work Step by Step
The formula for factoring the sum of two cubes is: $A^3+B^3=(A+B)(A^2-AB+B^2)$.
The formula for factoring the difference of two cubes is: $A^3-B^3=(A-B)(A^2+AB+B^2)$.
Hence here: $27x^3-8=\\=(7x)^3-2^3\\=(3x-2)((3x)^2+3x\cdot2+2^2)\\=(3x-2)(9x^2+6x+4)$