Correct Answer - Option 2 : 316

**Given:**

a - b = 4 and ab = 21

**Formula Used:**

a^{2 }+ b^{2} = (a - b)^{2} + 2ab

a^{3} - b^{3} = (a - b)(a^{2} + b^{2} + ab)

**Calculation:**

As, a - b = 4 and ab = 21

Now, a2 + b2 = (4)2 + 2 × 21 = 16 + 42 = 58

a3 - b3 = (4)(58 + 21) = 4 × 79 = 316

**∴ The value of a3 - b**^{3} is 316.