This is just a guess, which must be supported by mathematical induction. After investigation, four planes can only divide the space into 15 parts (three planes can divide eight spaces into two parts, and the fourth plane can't divide all eight planes into two parts), so the answer given on the second floor is wrong.

We know that n straight lines can be divided into 1+n(n+ 1)/2 planes at most. I think it has something to do with the number of n plane subspaces.

N-line plane subspace

1 2 2

2 4 4

3 7 8

4 1 1 15

We see that the number in the second column is equal to the sum of the number above it and the number on its left, and the number in the third column is equal to the sum of the number above it and the number on its left. Based on this, we finally get the result of 2+(n- 1) (n 2+n+6)/6.