I want to know, how it was possible to create the cubes, with their shinny, dark and cubed parts? I know it could be doable with Photoshop, but how? Is there any software better suited to make it than that?
To expand on Marc's answer I dug into the source code of the page.
That means there's a script, or numerous scripts that interact to move the images around the page. Off the top of my head I'd say, as I mentioned in my comment, that the images rely on the cursor's X and Y coordinates and adjust themselves according to the coordinates.
At the top of the source code we find a number of different scripts. One of them is called "jparallax" which traces back to this website, where you can find numerous demos.
From the web site's about page:
Given the way the image looks, my guess is that it was modelled in 3D Studio Max, rendered using V-Ray, possibly with some post production in Photoshop (it looks like the parallax effect was created by using 3 separate images, so a little tweaking in Photoshop may have been needed).