I wasn't quite sure what to expect when computing the BOM cost, so here's a rough estimation of the main costs.  This assumes a 16x baseboard populated with 16 Allwinner A20 cards with 1GB of RAM each.

- Case, power supply: $100

- 16 A20 processors: $125

- 32 4gbit DDR3 ics: $250

- 16 microSD cards, microSD card sockets: $120

- CPU-card voltage regulators: $60

- Management circuits: $30

- Ethernet switching fabric: $80

This comes out to around $750; it doesn't include everything so let's round up and say $1k BOM.  I think if this were to actually be produced, the prices could be brought down a fair amount -- most of these represent "retail" prices with little-to-no volume discount (ex $250 for 16GB of RAM seems quite a bit above wholesale).  Also I hope to eventually eliminate the need for the microSD cards: having 16 microSD cards is not only costly, but a management nightmare.  Imagine having to swap and re-flash 16 microSD cards every time you want to update the boot image.  The first step will be to make the image be a simple network boot shim, which hopefully does not get updated often (if at all).  Unfortunately the Allwinner chips can't boot directly from the network -- they need some sort of local bootloader.  Since the microSD cards would all contain the same data, it should be possible in theory to only have one copy of the data on the baseboard, and have the CPU cards boot from that.  I'm not sure if it's feasible to directly multiplex/demultiplex an SD card, but it might be possible to use the SPI-boot capability of the chips and use an FPGA to handle the booting.  For now, though, it's far easier to just include a microSD card per CPU card.

The prices here don't include the PCB costs; unfortunately, getting 4-layer mini-ITX-sized (17x17cm) boards made is decently expensive at any quantity.