Okay, I think that I have it.
The basic problem is that your armature doesn’t animate your cube an an armature–your cube spins in Blender because it’s a child of the armature. Indeed, try removing the “armature modifier” that you have on the cube–you should find that the cube still spins–because that modifier isn’t currently doing very much.
What I suggest is this:
First, unparent the cube from the armature–that is, make it no longer a child of the armature.
Next, in the 3D view, switch from “Object mode” to “Weight Paint” (via the dropdown menu at the bottom of the 3D view). In this mode, select the relevant bone in your armature, then paint the cube.
This “painting” tells Blender–and Panda–how the vertices are controlled by the armature: blue indicates no control, red indicates full control. (Values in-between blue and red only have much meaning if more than one bone controls a given vertex, in which case they indicate the weight given to those respective bones.)
You should find that the cube once again follows the motions of the bones of your armature.
Now, you may well find that your animation no longer works. I’m not sure of the specifics, but my best guess is that this is because it was made before the cube was properly controlled by the armature.
As a result of this, you may find that deleting and re-making your animation is called for.
Once all of this is done, try once again exporting your model. (And for safety’s sake, let me note that both the model and the armature should be selected when you do!) Hopefully, you should find your animation working at last!
