If x = 255, y = 256, z = 257, then find the value of x3 + y3 + z3 - 3xyz.

Answer: Option B

$$\begin{array}{rl}& x^3+y^3+z^3-3xyz\\ & =\frac{\left(x+y+z\right)}{2}\left[{\left(x-y\right)}^2+{\left(y-z\right)}^2+{\left(z-x\right)}^2\right]\\ & =\frac{255+256+257}{2}\left[1^2+1^2+2^2\right]\\ & =\frac{768\times 6}{2}\\ & =\frac{4608}{2}\\ & =2304\end{array}$$