Rolling the Cube Once More

A cube with sides of size 1×1 is placed on an n×n grid where each cell contains a number between 1 and 6. We want to roll the cube on this grid.

Let's assume a 4×4 grid is given as follows:

Initially, each face of the cube has numbers from 1 to 6 written on it, and the cube will be rolled one cell at a time for m times.