Answer
$(5x-2)(25x^2+10x+4)$
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: $125x^3-8=\\=(5x)^3-2^3\\=(5x-2)((5x)^2+5x\cdot2+2^2)\\=(5x-2)(25x^2+10x+4)$