Scientists explain how wombats drop cubed poop

That link is well worth reading about why they do it. There's no paper yet, but this, from the abstract[0], addresses how:

"In the final 8 percent of the intestine, feces changed from a liquid-like state into a solid state composed of separated cubes of length 2 cm. This shape change was due to the azimuthally varying elastic properties of the intestinal wall. By emptying the intestine and inflating it with a long balloon, we found that the local strain varies from 20 percent at the cube's corners to 75 percent at its edges. Thus, the intestine stretches preferentially at the walls to facilitate cube formation. This study addresses the long-standing mystery of cubic scat formation and provides insight into new manufacturing techniques for non-axisymmetric structures using soft tissues."

Incidentally, I grew up in the Australian bush, about halfway between Sydney and Brisbane, but never saw a wombat. (But often cockatoos, kookaburras, rainbow lorikeets, spiders, ticks, leeches, snakes, wallabies, possums, and once a tiger cat (tiger quoll) got into the chook pen.) On a recent holiday to a tiny village near Canberra, everyone had stories about wombats taking up residence in or under their houses, and I saw quite a few dead on the side of roads.

[0] http://meetings.aps.org/Meeting/DFD18/Session/E19.1