What is the next term to complete the given analogy?
$$\text{B}:16::\text{E}:?$$

Let's find the mathematical logic behind the first pair $\text{B}:16$:
The alphabetical positional index of the letter B is $2$.
Notice that $2^4=16$. So the pattern follows ${\text{Position}}^4$.

Now, let's apply the same pattern to the letter E:
The alphabetical positional index of the letter E is $5$.
Using the exact logic:

$$\text{Value}=5^4=5\times 5\times 5\times 5=625$$

Thus, the missing term is $625$.