Yes that's a little out of control, mostly because it'll soon be next to impossible to modify the shape with any time efficiency. The less points you have to push and pull the faster of a modeller you will become. Also you don't need anywhere near this many faces to describe the form you are modeling. So you can set this aside for now (save it) and start a new file. It's a bit of a mindbender but I think it will save you time in the end and you'll be more in control, and learn an armada of new tricks
The goal is to start with the simplest geoform (cubes, spheres, cones etc) with the fewest number of faces you possibly can to as closely match the shape you are about to model.
When you model you can have the channelbox open. Create a cube and have a look there. You'll see
Click the polyCube1 and you'll see subdivisions width, height and depth. Set these three to a value of 1. Now you have all the faces you need to describe a cube.
Move it to the side and make another cube, this time set the three subdivisions to a value of 3. Voila. Instant rubiks cube. Underdetailed but both of these cubes serves as a good starting point. It's up to you to try the method you like better. Start with a building component (the 1 cube) or start with the whole shape (the three subdivisions)
PS: The inside of the cube is never seen unless you take it apart with force hehe. I wouldn't model it but then again I am always looking for shortcuts :]
Have fun now.