All right, in the modifier, did you select your armature (so that the modifier knows which armature should be used)? If not, go to the modifier and click on the box labelled “Object”; that should produce a drop-down menu from which you should be able to select your armature. Make sure that you [b]don’t[b] click on “Apply” or “Apply as Shape Key”.
That done, you should probably weight-paint the vertices of your cube: put the armature into “Pose” mode (in the main 3D view, click on the menu that should read “Object Mode” and select “Pose Mode” from the menu that should appear. Then select your cube and, from the same menu, select “Weight Paint”. In that mode paint all of your cube’s vertices until they’re no longer blue.
Finally, go back to “Object Mode”, select both the cube and the armature and have another shot at exporting.