8. (10 points) For a two-digit number $n$, A, B, C, and D have the following conversation:
$A: “ n$ is divisible by $2^{4}.$”
$B: “ n$ is divisible by $3^{3}.$”
$C:$ “ $n$ is divisible by $6^{2}.$”
$D$ : “ The sum of the digits of $n$ is 15.”
Only two of them are correct. What is the value of $n$? $\qquad$
【Analysis】Among four people, only two are telling the truth. Both $B$ and $C$ require the sum of the digits of $n$ to be a multiple of 9, which contradicts what $D$ says. By finding the common points, differences, and contradictions in the four statements, we can determine who is telling the truth.

【Solution】According to the analysis, both $B$ and $C$ require the sum of the digits of $n$ to be a multiple of 9. However, $C$ requires the sum of the digits of $n$ to be 15. If $D$ is correct, then $B$ and $C$ are incorrect, so $A$ must be correct, and $n = 2^4 \times 3 = 96$. If $D$ is incorrect, then the least common multiple of $2^4$ and $3^3$, $6^2$ and $3^3$, or $2^4$ and $6^2$ would all be greater than 100, which is a contradiction. Therefore, the value of $n$ is 96.

The answer is: 96.