25. E.

Notice that, $2^{8}+1=257, 6^{3}=216, 7^{3}=343, 2^{18}=\left(2^{6}\right)^{3}=64^{3}$.
Thus, $64^{3}$ is the largest cube number less than $2^{18}+1$. Therefore, the number of cube numbers between $2^{8}+1$ and $2^{18}+1$ is $64-7+1=58$.
25. Between $2^{8}+1$ and $2^{18}+1$, there are $(\quad)$ perfect cubes.
(A) 4
(B) 9
(C) 10
(D) 57
(E) 58