$$\frac{{\left[ {\left( {888 \times 888 \times 888} \right) - \left( {222 \times 222 \times 222} \right)} \right]}}{{\left[ {\left( {888 \times 888} \right) + \left( {888 \times 222} \right) + \left( {222 \times 222} \right)} \right]} }=\, ?$$

$$\eqalign{ & \frac{{\left[ {\left( {888 \times 888 \times 888} \right) - \left( {222 \times 222 \times 222} \right)} \right]}}{{\left[ {\left( {888 \times 888} \right) + \left( {888 \times 222} \right) + \left( {222 \times 222} \right)} \right]}} \cr & = \frac{{\left( {{{888}^3} - {{222}^3}} \right)}}{{\left[ {{{888}^2} + \left( {888 \times 222} \right) + {{222}^2}} \right]}} \cr & = 888 - 222 \cr & = 666 \cr} $$