have you tried blend shape deformer?
in this case...you take your cube...duplicate it how ever many times you want...
then with the duplicates...model how you want the cube to melt....
then you use the blendshape deformer found in the animation section of maya go to DEFORM> CREATE BLENDSHAPE open the option box...and choose IN BETWEEN....this will make the cube melt into the steps that you modelled...you'll have okay control over the way it melts too...
anyways...good luck...sounds cool
-peace-
aken009