I'll start with a couple of assumptions:

1. we cannot rearrange the pieces between cuts (confirmed by OP in the comments)
2. each guest needs to get the same amount of cake and frosting, else the split isn't equal.

With these assumptions, we are best off by keeping each cut vertical, and running through the center of the cake.

So let's see what we can get. Seems like the obvious place to start is the "split to eight", because we get that with only four cuts. To keep the math in integers, let's decide the cake's size is 504 units.

Since we need to be able to split the cake into 9 pieces of 56 too, we'll have at least one cut running though each of the pieces. We should probably try to make 56 the biggest piece too, so we'll cut 7 off one of the pieces. Since it costs nothing extra, we'll run the cut all the way through the cake; even though we aren't likely to be able to use the other 56, having the extra pieces might be useful in some other way.

Then we should probably make a 49, so we can build another 56 with the 7. Let's cut it from the piece next to the seven for clarity:

Continuing in the same manner, let's make a "friend" for 14, and then for the resulting 21 too:

Now would you look at that! We are left with exactly two 28s, which sum up to exactly the required amount for the 9th person! (This probably didn't come as a surprise to you, if you were paying attention to what we were doing.) So with 8 cuts we have accommodated both 8 and 9 persons:

Then, let's see what we need in order to combine these into pieces of size 72.

Our "numbers of interest" are whatever's needed to complete the other pieces to 72, so let's list them all. We'll not need all of them, since we are going to split some to fill the others.

Piece Needs
56    16
49    23
42    30
35    37
28    44
21    51
14    58
 7    65

Looking at the list, we have multiples of 7 on the left, and 2 more than multiples of 7 on the right, and if we match the lists to each other, it becomes clear that we get the list on the right by adding 9 to the list on the left and reversing it.

A simple way to turn the list on the left to the list on the right is to pair the pieces up to 70 sized chunks (we can make exactly 7 such pairs), and then split the 7 sized bits into {2,2,2,1}s, giving us exactly the required 7 lots of 2. That would bring us to

11 cuts in total

If there's a better method, I couldn't find it right now.

So here's the final cake: