The value of $$\frac{(13)^3-4^3 }{(13 - 8 ÷ 2)}÷8-\{2+6×9\}$$​  is:

Correct option is A

Given:

​$$\frac{13^3 - 4^3}{13 - \frac{8}{2}} \div 8 - \{2 + 6 \times 9\}.$$​​

Formula Used:

$$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$$​.

Solution: ​

Simplifying terms separately:  
$$13^3 - 4^3 = (13 - 4)(13^2 + 13 \times 4 + 4^2) = 9 \times (169 + 52 + 16) = 9 \times 237 = 2133$$​

$$13 - \frac{8}{2} = 13 - 4 = 9$$

So, 

$$\frac{13^3 - 4^3}{13 - \frac{8}{2}} = \frac{2133}{9} = 237$$ 

$$237 \div 8 = \frac{237}{8}$$ 

$$2 + 6 \times 9 = 2 + 54 = 56$$  

Now, 

$$\frac{237}{8} - 56 = \frac{237 - 448}{8} = \frac{-211}{8}$$ 

Thus, the value of expression is $$\frac{-211}{8}$$ ​