As you know from the way people pack their belongings in cardboard boxes, and not in exercise balls, when they move, cubes can be more efficiently packed together than spheres can. A neutron star made of cubic neutrons could hold 24% more of them than it could if it were composed only of spherical neutrons.
What kind of density could cause a subatomic particle to squish into a different shape?
10,000,000,000,000,000 grams per cubic centimeter. For comparison, that is
10,000,000,000,000,000 times more dense that the human body.
Felipe J. Llanes-Estrada, & Gaspar Moreno Navarro (2011). Cubic neutrons arXiv arXiv: 1108.1859v1