\(y^6-64x^6\)
\(=\left(y^3\right)^2-\left(8x^3\right)^2\)
\(=\left(y^3-8x^3\right)\left(y^3+8y^3\right)\)
\(=\left(y-2x\right)\left(y^2+2xy+4x^2\right)\left(y+2x\right)\left(y^2-2xy+4x^2\right)\)
\(=\left(y^2-4x^2\right)\left[\left(y^2+4x^2\right)^2-4x^2y^2\right]\)
\(=\left(y^2-4x^2\right)\left(y^4+8x^2y^2+16x^2-4x^2y^2\right)\)
\(=\left(y^2-4x^2\right)\left(y^4+4x^2y^2+16x^2\right)\)