I created the first animation entirely within the GIMP, using Filters / Distort / Map Object for mapping an image to a box, and Script-Fu / Shadow / Drop Shadow for the shadow effect. If you are curious about the parameters to Map Object, here they are: I set the X angle to 30 degrees, the Z angle to 0 degrees, and I changed the Y angle from 0 to 90 degrees in eight steps, in order to get the rotating box effect. I enabled the options "Transparent Background" and "Create New Image", and I used the default values for everything else.

The background is the standard "Dried Mud" pattern... Nothing special about that.

After running my script to merge the background with the animation, I get a nice rotating cube on top of a fancy background. Note that the shadow effect would not have been possible if I had taken the first animation and put it over a textured background in a web page, because the GIF format does not support partial transparency.

We can of course do more with this animation...