\(C=\left(2x+y\right)^3-6\left(2x+y\right)^2\cdot x+12\left(2x+y\right)\cdot x^2-8x^3\)
\(=\left(2x+y\right)^3-3\cdot\left(2x+y\right)^2\cdot2x+3\cdot\left(2x+y\right)\cdot\left(2x\right)^2-\left(2x\right)^3\)
\(=\left(2x+y-2x\right)^3=y^3\)
\(C=\left(2x+y\right)^3-6\left(2x+y\right)^2x+12\left(2x+y\right)x^2-8x^3\\ =\left(8x^3+12x^2y+6xy^2+y^3\right)-6x\left(4x^2+4xy+y^2\right)+12x^2\left(2x+y\right)-8x^3\\ =8x^3+12x^2y+6xy^2+y^3-24x^3-24x^2y-6xy^2+24x^3+12x^2y-8x^3\\ =\left(8x^3-8x^3-24x^3+24x^3\right)+\left(12x^2y+12x^2y-24x^2y\right)+\left(6xy^2-6xy^2\right)+y^3\\ =y^3\)
