mathematics - A closed path on the Rubik's cube

Is it possible to draw a closed path on the surface of a standard $3\times3\times3$ Rubik's cube

• such that the path traverses each of the $54$ little squares exactly once, and


• such that the path does not go through any corner of these little squares?

Answer

An observation is..

that you can traverse a cube's face from one corner and end up diagonally opposite or in same column (or row).

Using this observation, one of many possible solutions is (left image is front of cube, right image is inside view):