\(a)8x^6-27y^3=\left(2x^2\right)^3-\left(3y\right)^3=\left(2x^2-3y\right)\left(4x^4+6x^2y+9y^2\right)\)
\(b)\left(x+3\right)^3-8=\left(x+3\right)^3-2^3\)
\(=\left(x+3-2\right)\left[\left(x+3\right)^2+2\left(x+3\right)+4\right]\)
\(=\left(x+1\right)\left(x^2+6x+9+2x+6+4\right)\)
\(=\left(x+1\right)\left(x^2+8x+19\right)\)
\(c)x^6-y^6=\left(x^3\right)^2-\left(y^3\right)^2=\left(x^3+y^3\right)\left(x^3-y^3\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2\right)\left(x-y\right)\left(x^2+xy+y^2\right)\)
\(d)x^3+12x^2+48x+64=x^3+3x^2\cdot4+3x\cdot16+4^3\)
\(=\left(x+4\right)^3\)