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

it from previous year ssc papers, 0 is the right answer

Using (x) of Basic Formulae

If $a + b + c = 0$, then

$\large a^3 + b^3 + c^3 = 3abc $

Here, $\large 0.111 + 0.222 + (–0.333) = 0$

$\large \therefore (0.111)3 + (0.222)3 + (–0.333)3$

$\large= –3 × 0.111 × 0.222 × 0.333$

$\large= – (0.333)2 × 0.222$

$\large\therefore$ Expression

$\large = [–(0.333)2 × 0.222 + (0.333)2 × 0.222]3 = 0.$