Select the option that is related to the third number in the same way as the second number is related to the first number.
3 : 67 :: 6 : ?

Given, 67 is related to 3

The logic here is

$$3+\left(3+1\right)^3=3+4^3=67$$  $$\longrightarrow\ $$  $$\text{first number}+\left(\text{first number}+1\right)^3=\text{second number}$$

Similarly,

$$6+\left(6+1\right)^3=6+7^3=349$$  $$\longrightarrow\ $$ $$\text{first number}+\left(\text{first number}+1\right)^3=\text{second number}$$

$$\therefore\ $$349 is related to 6 in the same way 67 is related to 3.

Hence, the correct answer is Option A