You could turn all 3 planes low, and turn one column high, lighting up all 3 LEDs, however, if you are resistored to drive your LEDs at 20mA, and you run 3 LEDs off one controller pin, you will be running 60mA on a device rated for 40, and will likely do damage to the microcontroller (if you run the leds at 10mA, you would be within spec.
You dont need to run the cube that way, the way you normally run a cube is by cycling through each layer, and lighting up just the LEDs in that layer that you want lit, then moving to the next layer. The LEDs appear to all be lit at the same time because of persistence of vision, but they are actually flashing on and off very quickly.
What i was referring to was the way you control the LEDs, there are many ways to do it, but will probably want to run things in loops things in sequence, but technically you dont have to do it that way.