This is actually kind of fun. Math was never my strong suit though, I struggled with calculus.
but using D instead of dimension, here are the figures for 1-4 D cubes.
3D cube has 6 2D sides, 12 1D lines, and 8 0D vertices for example
1D - 2 0D
2D - 4 1D, 4 0D
3D - 6 2D, 12 1D, 8 0D
4D - 8 3D, 24 2D, 16 1D, 16 0D
5D - 10 4D, X 3D, X 2D, X 1D, 32 0D
Looking at that, if N is the dimension in question, then N-1 = N*2 and 0D = 2^N. So I came up with 10 different 4D tesseracts and 32 vertices. But I was only able to guess the values for 4D and 0D based on those patterns. I wasn’t able to guess how to get the other values until I found out what they were.
Looking online, I found the values for 3D, 2D and 1D for a 5D cube.
In five-dimensional geometry, a 5-cube is a name for a five-dimensional hypercube with 32 vertices, 80 edges, 80 square faces, 40 cubic cells, and 10 tesseract 4-faces.
So that matches the 4D and 0D values. Looking at the info, it seems like the value for the middle D values is the previous dimensions middle D value * N.
So if you want the 2D values of a 4D tesseract, its is the number of 2D values in a 3D cube*N, which is 6x4
If you want the 3D values of a 5D cube, its 8*5.