This board could do it for you.
Its basically an Arduino (uses external USB/Serial adapter to load up a sketch, or load via the ICSP header) and up to 12 TPIC6B595 drivers that can sink lots of current. 96 outputs available if all parts are populated.
So you'd make up 8 layers of 64 LEDs. Each layer would have a common anode, and the 64 cathodes would go to a current limit resistor and then a TPIC6B595 output. Each LED in a column would have its cathode connected to the one above it.
One anode at a time is turned on to supply current to the layer - use a P-channel MOSFET with its Gate pulled low by a TPIC6B595 output to turn it on, and a pullup resistor to +5 toturn it off.
If all 64 LEDs are turned at max current of 20mA, that'd need 1.28A. This MOSFET would do nicely; with on-resistance of 0.041 ohm at 4.5V switching levels, the part would dissipate 0.041ohm * 1.28A = 53mW of power, so heat sinking would not be needed.http://www.digikey.com/product-detail/en/NDP6020P/NDP6020P-ND/1055922
SPI.transfer()'s are used to control the shift registers.
To control the multiplexing, every 4mS you would do a set of transfers:
digitalWrite (outputEnable, HIGH); // turn off all drivers
digitalWrite (slaveSelect, LOW);
SPI.transfer (anodeSelect); // 1 of 8 bits would be low
digitalWrite (slaveSelect, HIGH); // moves data to output drive latch
digitalWrite (outputEnable, LOW); // turn on all drivers
The digitalWrites could be replaced with direct port manipulations also to really speed things up.
For this particular card, outputEnable is on PB1 and slaveSelect is on PB2:
PORTB = PORTB | B00000010; // makes PB1 high
PORTB = PORTB & B11111011; // makes PB2 low
PORTB = PORTB | B00000100; // makes PB2 high
PORTB = PORTB & B11111101; // makes PB1 low
The rest of the 4mS, you'd prep your data for the next write out. update the anodeSelect for the next layer, etc.
Receiving data from the serial port, reading buttons, doing math for fancy ripples, whatever.
I just got 10 in, $6 for a bare board mailed to US locations, overseas a little more, depends on the country.
Build up as you wish with sockets or no, male/female headers or just wire right to the board, etc.
paypal is fine for payment.