Correct Answer - Option 4 : 36

**Concept**:

The general form of a cubic equation is : f(x) = ax^{3} + bx^{2} + cx + d = 0. And the cubic equation has the form of ax^{3} + bx^{2} + cx + d = 0, where a , b and c are the coefficients and d is the constant .

**Calculation** :

Given, x^{3} - 6x^{2} + 11x - 6 = 0

⇒ (x - 1) is one of the factors.

By dividing x^{3} - 6x^{2} + 11x - 6 by (x - 1),

⇒ (x - 1) (x^{2} - 5x + 6) = 0

⇒ (x - 1) (x - 2 ) (x - 3) = 0

This of the cubic equation solution are x = 1, x = 2 and x = 3.

Sum of cubes = A^{3 }+ B^{3 }+ C^{3}

A = 1, B = 2 and C = 3

⇒ A^{3 }+ B^{3 }+ C^{3} = (1)^{3} + (2)^{3} + (3)^{3}

⇒ 1 + 8 + 27

⇒ **36**