  The 30 MacMahon colored cubes have each face painted with one of six colors
and every color appears on at least one face. One puzzle involving these cubes
is to create a $2\times2\times2$ model with eight distinct MacMahon cubes to
recreate a larger version with the external coloring of a specified target
cube, also a MacMahon cube, and touching interior faces are the same color.
J.H. Conway is credited with arranging the cubes in a $6\times6$ tableau that
gives a solution to this puzzle. In fact, the particular set of eight cubes
that solves this puzzle can be arranged in exactly \textit{two} distinct ways
to solve the puzzle. We study a less restrictive puzzle without requiring
interior face matching. We describe solutions to the $2\times2\times2$ puzzle
and the number of distinct solutions attainable for a collection of eight
cubes. Additionally, given a collection of eight MacMahon cubes, we study the
number of target cubes that can be built in a $2\times2\times2$ model. We
calculate the distribution of the number of cubes that can be built over all
collections of eight cubes (the maximum number is five) and provide a complete
characterization of the collections that can build five distinct cubes.
Furthermore, we identify nine new sets of twelve cubes, called Minimum
Universal sets, from which all 30 cubes can be built.
