Once you have defeated the boss Planestrider (The big face inside the cube) and received the Monolith of the Plans, of course you can the Cube as bed inside a house of your own.
In your house just put The Supreme Cube on the floor and right click on it to select what you want to train. Be careful, if you use it inside your backpack, you will be teleported inside the cube.
While your character is sleeping The Supreme will take another form, (A little black cube). To return it to normal, just use it.