Answer
$(x+1)(x^2-x+1)(x+2)(x^2-2x+4)$
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: $x^6+9x^3+8=\\=x^6+x^3+8x^3+8\\=x^3(x^3+1)+8(x^3+1)\\=(x^3+1)(x^3+8)\\=(x^3+1^3)(x^3+2^3)\\=(x+1)(x^2-x+1)(x+2)(x^2-2x+4)$
