LED Cube with no transistors
Each layer is tied into a single 100 ohm resistor. This limits the total current for the 16 leds in a layer to 20 mA total, in theory. As the internal resistance of the atmega pin also changes the available voltagr based on the current passed, the actual current may be slightly lower.

Since its limited to 20mA, the pin would not blow and there is no need for a transistor to allow a higher current carrying capacity. And each led can still be bright at 1.25 mA each in parallel.