Complete the analogy:
$$8:256::27:\_\_\_\_\_\_\_\_$$

Let's decipher the prime power exponential relationship mapping the first term to the second term:
* The first number is a perfect cube: $8=2^3$.
* The corresponding mapped number is: $256=2^8$.

Following this identical logic pattern for the second pair where the number is $27$:

* Express 27 as a perfect cube: $27=3^3$.
* Therefore, the missing term must be $3$ raised to the power of $8$:

$$3^8=6561$$