A 2-layer (size 2) cube has corner cubies only.
Cubes of size 2 and size 3 have single solutions meaning that all the cube elements can have only one correct location for a solved cube.
Centre cubies differ from the corner and edge cubies in that their orientation or position has multiple possibilities. For cubes of odd size, there will be a centre cubie that is centrally located on the cube face and that cubie has only one correct location for a solved cube. However, multiple locations of all other centre cubies apply for a solved cube. The centre cubies (other than the single central one for cubes of odd size) form sets-of-four on each face and sets-of-24 for the whole cube for the various orbits. These centre cubies have four possible final positions (their orientation changes with position but cannot be changed independently) that would satisfy the solved state.
For a detailed analysis of the number of possible states for cubes without or with marked centres refer to cubestates.pdf.