\(\left(a-1\right)^3-\left(a+1\right)^3\)
\(=\left[\left(a-1\right)-\left(a+1\right)\right]\left[\left(a-1\right)^2+\left(a-1\right)\left(a+1\right)+\left(a+1\right)^2\right]\)
\(=\left(-2\right)\left(a^2-2a+1+a^2-1+a^2+2a+1\right)\)
\(=\left(-2\right)\left(3a^2+1\right)\)