3 ( 333 )^3 + ( 333 )^3 + ( 334 )^3 - 3 × 333 × 333 × 334 is equal to = ?

Answer: Option C

According to question
$$\text{root}3\text{of}{\left(333\right)}^3+{\left(333\right)}^3+{\left(334\right)}^3-3\times 333\times 333\times 334$$
As we know that
a³ + b³ + c³ - 3abc
= $$\frac{1}{2}$$ (a + b + c)[(a - b)² + (b - c)² + (c - a)²]
= $$\frac{1}{2}$$ (333 + 333 + 334)[(333 - 333)² + (333 - 334)² + (334 - 333)²]
= $$\frac{1}{2}$$ × 1000[0 + 1 + 1]
= $$\frac{1}{2}$$ × 1000 × 2
= $$\text{root}3\text{of}1000$$
= 10