Answer
$(x^3-2)(x+2)(x^2-2x+4)$
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:
$6x^3+x^6-16=\\=x^6-2x^3+8x^3-16=\\=x^3(x^3-2)+8(x^3-2)\\=(x^3-2)(x^3+8)\\=(x^3-2)(x^3+2^3)\\=(x^3-2)(x+2)(x^2-2x+4)$
