Cubic projection is essentially the same as Planar, except that you cannot select a Texture Axis. Cubic projects the image from all three axes at the same time. The image is projected like Planar, except simultaneously along all three axes. Use Cubic when you wish to apply the same image to all sides of a rectangular shape, such as an image of tiling bricks wrapped around the sides of a building, or wallpaper on the walls of a room.
Note that Cubic Projection projects along the X, Y and Z axes and objects merely intersect these projections. This means that images like text will only be correct on three sides, the others will be reversed as shown here with the images that have the arrow coming out of them rather than going in. Creating an item like a dice needs six planar projections to be correct.