Which of the following is the value of $\frac{231\times 231\times 231-131\times 131\times 131}{231\times 231+231\times 131+131\times 131}$?

The given numerical expression mirrors the standard algebraic form by letting $a=231$ and $b=131$:
$$\text{Expression}=\frac{a^3-b^3}{a^2+ab+b^2}$$

Applying the identity for the difference of two cubes, $a^3-b^3=(a-b)(a^2+ab+b^2)$:

$$\text{Expression}=\frac{(a-b)(a^2+ab+b^2)}{a^2+ab+b^2}$$

Canceling out the matching quadratic trinomial factor from both the numerator and denominator reveals:

$$\text{Expression}=a-b$$

Substituting back the values assigned to $a$ and $b$:

$$\text{Value}=231-131=100$$