mid-15c., "being of the third power;" 1550s, "having the form of a cube," from Old French cubique (14c.), from Latin cubicus, from Greek kybikos, from kybos "cube" (see cube (n.)). Meaning "solid, three-dimensional" is from 1650s.
Cubical is attested from 1590s with the meaning "of or pertaining to a cube," and according to OED it is "Now more usual than cubic in this sense." Related: Cubically.