[math-fun] Packing puzzle

Consider a 3-D tile made of 5 cubies arranged like a P-pentomino, 1 cubie thick. You pack these into a 3x3 cube (together they fill all but 2 cubies). Suppose one of the unpacked cubies is the center cubie. Can the remaining unpacked cubie be at a vertex of the 3x3? An edge? A face center?