How is it wired up so far? Anodes connected in columns, cathodes connected in layers?
So 64 anodes would be driven high by 8 shift registers (thru current limit resistors) and you'll add a 9th shift register to control 8 N-channel MOSFETs to sink the current (up to 64 * 20mA = 1.28A) from 1 layer at a time?
Shift registers controlled by SPI.transfer() commands for nice fast updating?
5V, 2A power supply like this would be sufficient.http://www.dipmicro.com/store/DCA-0520
Use 1 resistor per anode column, value of (5V - (Vf of LED, ~1.7V for Red?) )/20mA = 165 ohm , 180 is standard value and would work well.
Use Low Rds, Logic Level N-channel MOSFETs such ashttp://www.digikey.com/product-detail/en/NTD5867NL-1G/NTD5867NL-1GOS-ND/2401422
turn all cathode off, drive the anodes, turn 1 cathode on, in 5mS turn it off, drive anodes for next layer, turn next cathode on, in 5mS turn it off, repeat for next 6 layers.
During the 5mS, your code can be doing something else.