\(8x^3+(1-3x)^3+(x-1)^3\\=8x^3+[1^3-3\cdot1^2\cdot3x+3\cdot1\cdot(3x)^2-(3x)^3]+(x^3-3\cdot x^2\cdot1+3\cdot x\cdot1^2-1^3)\\=8x^3+(1-9x+27x^2-27x^3)+(x^3-3x^2+3x-1)\\=8x^3+1-9x+27x^2-27x^3+x^3-3x^2+3x-1\\=(8x^3-27x^3+x^3)+(27x^2-3x^2)+(-9x+3x)+(1-1)\\=-18x^3+24x^2-6x\)
\(8x^3+\left(1-3x\right)^3+\left(x-1\right)^3\)
\(=\left(2x\right)^3+\left(1-3x\right)^3+\left(x-1\right)^3\)
\(=\left(2x+1-3x\right)^3\left[\left(2x\right)^2-2x\left(1-3x\right)+\left(1-3x\right)^2\right]+\left(x-1\right)^3\)
\(=\left(-x+1\right)^3\left(4x^2-2x+6x^2+9x^2-6x+1\right)+\left(x-1\right)^3\)
\(=\left(x-1\right)^3\left(-19x^2+8x-1\right)+\left(x-1\right)^3\)
\(=\left(x-1\right)^3\left[-19x^2+8x-1+1\right]\)
\(=\left(x-1\right)^3\cdot\left(-19x^2+8x\right)\)
\(=-x\left(19x-8\right)\left(x-1\right)^3\)
