\(\left(x+4\right)^3+\left(x+6\right)^3\)
\(=\left(x+4+x+6\right)\left[\left(x+4\right)^2-\left(x+4\right)\left(x+6\right)+\left(x+6\right)^2\right]\)
\(=\left(2x+10\right)\left(x^2+8x+16-x^2-10x-24+x^2+12x+36\right)\)
\(=2\left(x+5\right)\left(x^2-x^2+x^2+8x-10x+12x+16-24+36\right)\)
\(=2\left(x+5\right)\left(x^2+10x+28\right)\)