\(\left(x^2-x+1\right)\left(x^2+x+1\right)\left(x^2-1\right)\)
\(=\left(x^2-x+1\right)\left(x^2+x+1\right)\left(x-1\right)\left(x+1\right)\)
\(=\left(\left(x+1\right)\left(x^2-x+1\right)\right)\left(\left(x-1\right)\left(x^2+x+1\right)\right)\)
\(=\left(x^3+1^3\right)\left(x^3-1^3\right)=\left(x^3\right)^2-\left(1^3\right)^3=x^6-1\)