Cardinal Red (Solution)
by Derek Kisman, based on an idea by Amos Eshel
Using the orientation given in the puzzle page (i.e. the RWB corner is on top), one can use each of the corresponding cardinal directions to replace a single letter in the answer on that cubelet. These replaced letters spell out the answer SLEDDING when read in a circle.
BASSIST → BASSINET SHLEP → SHEEP EXTANT → SEXTANT DEDITION → SEDITION DAMP → SWAMP BOIL → BOWL UNARY → UNWARY CONTIGUOUS → CONTINUOUS