There are a lot of conditions you are not stating. You are obviously requiring that the slices be by integer steps.

If you have a cube n by n by n and split it horizontally at height h, and vertically at width k, then the four parts you divide the cube into are h by k by n, n-h by k by n, h by n-k by n, and n-h by n-k by n. those have volume nkh, (n-h)kn, h(n-k)n, and (n-h)(n-k)n. h and k can be any integers greater than 0 and less than n.

What you are noting is that if n= 3, then we can take you can take h= 1 and k= 1 so that nkh= 3(1)(1), (n-h)kn= 2(1)(3)= 6, h(n-k)n= (1)(2)(3)= 6, and (n-h)(n-k)(n)= 2(2)(3)= 12. But if n= 2 the only possible value for h and k is 1. Then nkh= 2(1)(1)= 2, h(n-k)n= 1(1)(2)= 2, h(n-k)(n)= 1(1)(2)= 2, and (n-h)(n-k)n= 1(1)(2)= 2. That is, the only possible way to divide a 2 by 2 by 2 cube into four piecesby integersis to divide two sides in the middle.