The value of $$\frac{{1.6 \times 1.6 \times 1.6 - 0.6 \times 0.6 \times 0.6}}{{1.6 \times 1.6 + 1.6 \times 0.6 + 0.6 \times 0.6}}$$      is:

Solution(By Examveda Team)

$$\eqalign{ & \frac{{1.6 \times 1.6 \times 1.6 - 0.6 \times 0.6 \times 0.6}}{{1.6 \times 1.6 + 1.6 \times 0.6 + 0.6 \times 0.6}} \cr & = \frac{{{{\left( {1.6} \right)}^3} - {{\left( {0.6} \right)}^3}}}{{{{\left( {1.6} \right)}^2} + 1.6 \times 0.6 + {{\left( {0.6} \right)}^2}}} \cr & = \frac{{\left( {1.6 - 0.6} \right)\left\{ {{{\left( {1.6} \right)}^2} + 1.6 \times 0.6 + {{\left( {0.6} \right)}^2}} \right\}}}{{{{\left( {1.6} \right)}^2} + 1.6 \times 0.6 + {{\left( {0.6} \right)}^2}}} \cr & = 1.6 - 0.6 \cr & = 1 \cr} $$