How does this calendar thing even work?
With two cubes, you don't have enough sides (total 12) to give both cubes numbers 0-9.

Instead, each cube has its own numbers (there may be other permutations that work, too):


One cube (A) will have 0, 1, 2, 4, 5, 6.
The other (B) will have 0, 1, 2, 3, 7, 8.


Then each date is represented by how the cubes are used:


01-03: Cube A is 0, followed by cube B.
04-06: Cube B is 0, followed by cube A.
07-08: Cube A is 0, followed by cube B.
09: Cube B is 0, followed by cube A, on 6, upside-down.
10-13: Cube A is 1, followed by cube B.
14-16: Cube B is 1, followed by cube A.
17-18: Cube A is 1, followed by cube B.
19: Cube B is 1, followed by cube A, on 6, upside-down.
20-23: Cube A is 2, followed by cube B.
24-26: Cube B is 2, followed by cube A.
27-28: Cube A is 2, followed by cube B.
29: Cube B is 2, followed by cube A, on 6, upside-down.
30-31: Cube B is 3, followed by cube A.


And before you ask, no, I've never seen one of these, and thus I really have no citation. But given the fact that the cubes look like they can go in either order (since they have numbers on the side, they should come completely free), this seems like the most logical solution.