Patty
It looks to me like they put a round box in the middle and either double layered around the bottom "cake layer" or stacked 2 boxes (1 narrower than the other) for each cake layer
As for the top - you could cover the lid with one diaper (cut & draped to fit) and then attach your sock flowers to wire and poke the wire through the lid cover.
If you didn't care about using the interior space, I would suggest using coffee canisters (like Maxwell House) to create the cake since they come in the same height but 2 different widths. Surround the wider one with rolled up diapers tack into place with your hermie and then tie a wide ribbon around that layer. Put hot glue on the lid and glue to the smaller cannister. Surround the small cannister with diapers, tack and tie a wide ribbon around the layer. For the top layer, just create like your old single layer style - just make it narrow enough to fit on top. Pin through the plastic lid of the lower cannister to hold in place and decorate!