Oxidation state of metal ion in unit cell
Edge positions are those at the centre of an edge of the cube; i.e. in the middle between two closest corner positions. As such, there are 12 edge positions and each belongs to 4 unit cells giving us 3 metal ions.

The way the nitride positions are described is basically a verbose way of saying cubic close-packed or face-centred cubic. Therefore, we can redescribe the cation positions as ‘all octahedral voids except for the one in the centre of the unit cell’. Since there are 4 atoms per unit cell in ccp and 4 octahedral voids, that again gives us a $3:4$ ratio and thus $\ce{M3^{IV}N4}$.