8x8x8 multiplexed LED cube with an Arduino Mega 2560

Using Arduino LEDs and Multiplexing
187

Actually, if the data goes live only when the SS pin is turned back HIGH, then I think this should be enough to switch to the next horizontal LED plane (next multiplexing step):

void displayCurrentPlane ()
{
    digitalWrite (PIN_SS, LOW); //Start transferring data

    for (byte i = N - 1; i >= 0; --i) //Set up the LEDs inside the current plane
    {
        SPI.transfer (cubeData[currentPlaneIndex][i]);
    }

    SPI.transfer (~(1 << currentPlaneIndex)); //Turn on the current plane and turn off all other planes (current plane's bit is set to 0, all other bits are set to 1)

    digitalWrite (PIN_SS, HIGH); //Done transferring data
}