If x = 222, y = 223, z = 225, then the value of x³ + y³ + z³ is?

Explanation:-

$$\eqalign{ & {x^3} + {y^3} + {z^3} - 3xyz \cr & = \frac{1}{2}\left( {x + y + z} \right)\left[ {{{\left( {x - y} \right)}^2} + {{\left( {y - z} \right)}^2} + {{\left( {z - x} \right)}^2}} \right] \cr & = \frac{1}{2}\left( {222 + 223 + 225} \right)\left[ {{{\left( {222 - 223} \right)}^2} + {{\left( {223 - 225} \right)}^2} + {{\left( {225 - 223} \right)}^2}} \right] \cr & = \frac{1}{2}\left( {670} \right)\left( {1 + 4 + 9} \right) \cr & = \frac{1}{2} \times 670 \times 14 \cr & = 4690 \cr}$$