1) \(a^3+1=\left(a+1\right)\left(a^2-a+1\right)\)
2) \(a^3+6a^2+12a+8=\left(a+2\right)^3\)
3) \(8a^3+12a^2+6a+1=\left(2a+1\right)^3\)
4) \(27a^3-1=\left(3a-1\right)\left(9a^2+3a+1\right)\)
5) \(x^3-12x^2+48x-64=\left(x-4\right)^3\)
6) \(27a^3-54a^2+36a-8=\left(3a-2\right)^3\)