I will note here that this has only been tested on the Windows version of the game. I can't speak for the experience of doing this on a Mac or Linux machine.

If you want to contribute with the equivalent actions for those, feel free to hit me with 'em in the comments! You'll also help others.

NOTE: This has to be done while the game is closed. For your own safety.

Aside from the assets, a game has to find a way to store the player's saved data and configuration.
On Windows, this is often done through the hidden AppData folder on the drive.

To access your own computer's AppData, all you need to do is bring up the Run prompt (Win+R) and type in:
%AppData%
This will bring up an Explorer window with your AppData folder open.
TIP: You can also type this directly into the address bar in any Explorer window!

You'll notice that by default it also opens to a sub-folder named Roaming. There are essentially three different types of AppData, but I'm not enough of a tech nerd to explain their exact purpose. The one we're interested in is local AppData, so back up one layer and open the Local subfolder.
TIP: You can also open that folder directly by typing %LocalAppData% into the Run prompt / Explorer.

Once within, you should see a likely-to-be-long, long list of folders. Scroll down through the list and find one named precisely QUBE.
NOTE: If you own Q.U.B.E: 10th Anniversary Edition, you may also find a folder named QUBE_Remastered. That folder belongs to that game, and has a similar format - that is to say, this guide works for both Q.U.B.E 2 and Q.U.B.E 10th.

Q.U.B.E 2's AppData contains a bunch of things in it that we're not interested in, although what we're looking for is quite clearly marked. Navigate to Saved (the only subfolder there), then Config, then WindowsNoEditor.
You should then see a bunch of .ini files within describing a lot of what the game saves about itself.
We'll need Input.ini. You can open it with any text editor, so Notepad will do.

This file contains all of the control bindings for the game. Scroll down to the ActionMappings lines and hack away!

You may be getting crossed by the names given in the file. Most of them pertain to the editor and are Q.U.B.E Create's problem.
Here's a list of the important ones. Look at the "ActionName="?????"" part to figure out where everything belongs, and modify the corresponding "Key=???" part.

• "Jump": ...Well. Jump.
  
• "NextColor" and "PrevColor": Scrolling through the list of available color powers.
  
• "StartFirePrimary": In-game referred to as "Interact". Acting upon the environment.
  
• "StartFireSecondary": In-game referred to as "Place cube". Placing the color powers onto blank spots.

• Alphabet keys are referred to as their capital version. Numbers are typed as words (One for 1...). The space bar is SpaceBar.
  
• Mouse buttons are referred to as LeftMouseButton, RightMouseButton and MiddleMouseButton.
  
• Escape and Tab are called as you'd expect.
  
• Control (Ctrl), Alt and Shift have to have Left or Right appended to specify which side the key is on (e.g. LeftShift).
  
• Know any others? Help me by dropping them into the comments!

Go ahead and enjoy the game. Your mileage may vary on the story, but now you can somewhat reliably enjoy the various puzzles the game sets you through!

NOTE: After doing this, DO. NOT. Touch anything in the in-game Controls menu. It's likely to undo the entire process.
NOTE: The Controls menu will not reflect your bindings if you set them up this way. Ignore this, this is normal.