Evaluate the following products without multiplying directly

$93 \times 95$

Evaluate

$(153)^{2}$

Factorise $: 8 x^{3}+y^{3}-27 z^{3}+18 x y z$

If $x^{2}-10 x+21=(x+m)(x+n)$ then $m+n=\ldots \ldots \ldots$

Without actually calculating the cubes, find the value of each of the following

$\left(\frac{1}{2}\right)^{3}+\left(\frac{1}{3}\right)^{3}-\left(\frac{5}{6}\right)^{3}$