8x8x8 multiplexed LED cube with an Arduino Mega 2560

Using Arduino LEDs and Multiplexing
189

For the anode/layer, writing a 1 into the shift register bit makes the output go low & turns on the PNP to make the anodes High.
For each cathode, writing a 1 into the shift register bit to make the output go low and turn on the LED.

Can you seperate the SS for the anode from the SS for the cathodes?

Instead of your funny << shift thing, pull the data from an array:

for (layer = 0 to 7){
// turn off all layers
digitalWrite(AnodeSS, LOW);
  SPI.transfer(0x00);
digitalWrite(AnodeSS, HIGH);

// write cathode - I suppose this could be the array structure you have above too
digitalWrite(CathodeSS, LOW);
  SPI.transfer(cathodeData[2*layer]);        // 0,2,4,6,8,10,12,14
  SPI.transfer(cathodeData[(2*layer)+1]); // 1,3,5,7,9,11,13,15
digitalWrite(CathodeSS, HIGH);
// this seems simpler to me tho - just 2 bytes per layer

// turn on anode
digitalWrite(AnodeSS, LOW);
  SPI.transfer(anodeData[layer]);
digitalWrite(AnodeSS, HIGH);

}