You can't knife a theoretical cube so you must make it Editable (C key) - that step is what created polygons.
Now that you have polygons, faces and edges you can work in Polygon, Edge or Point Mode.

With the cube selected click the Live Selection icon which is also found in the Tool menu.
Set the Radius to 1 for accuracy. With 'Only Select Visible Elements' checked the Knife will not cut through the whole cube or sides.