The simplified value of $${\left[ {{{\left( {0.111} \right)}^3} + {{\left( {0.222} \right)}^3} - {{\left( {0.333} \right)}^3} + {{\left( {0.333} \right)}^2}\left( {0.222} \right)} \right]^3} = ?$$

Solution (By Examveda Team)

According to question,
As we know that a + b + c = 0
Then,
a³ + b³ + c³ - 3abc = 0
$$\therefore {\left[ {{{\left( {0.111} \right)}^3} + {{\left( {0.222} \right)}^3} + {{\left( { - 0.333} \right)}^3} - 3 \times 0.111 \times 0.222 \times \left( { - 0.333} \right)} \right]^3} = 0$$