1. Let the set $M=\{1,2, \cdots, 100\}, A$ be a subset of $M$, and $A$ contains at least one cube number, then the number of subsets $A$ that meet the requirement is $\qquad$
Solve: $2^{100}-2^{96}$.
From the problem, we know that set $M$ contains 4 cubic numbers: $1^{3}, 2^{3}, 3^{3}, 4^{3}$. The total number of subsets of $M$ is $2^{100}$, among which, the number of subsets that do not contain cubic numbers is $2^{96}$.
Therefore, the number of subsets containing cubic numbers is $2^{100}-2^{96}$.