How do you factor ##x^6-7x^3-8##?

Like this,

##x^6-7x^3-8 -= (x^3)^2 -7(x^3) -8 -= (x^3-8)(x^3+1) -= (x^3-(2)^3)(x^3+(1)^3)##

Recall that, ##a^3+b^3=(a+b)(a^2-ab+b^2)## and ## a^3-b^3=(a-b)(a^2+ab+b^2)##

##=> (x-2)(x^2+2x+4)(x+1)(x^2-x+1)##