Help verify 8x8x8 LED cube circuit
Based on comments it seems that limiting resistors will be necessary: one each between the P1-P8 LED state outputs and the LED arrays, for a total of 8 resistors. 

If 3.2V 20mA LEDs are used, then 100 Ohm resistors will be appropriate.

(5.0V-3.2V) ÷ 0.020A = 80 Ohms 
(rounded up to the next appropriate standard resistance value) = 100 Ohms


It could also be beneficial to hook up the reset pins on the CD4017's to the Arduino for control. The P1-P8 LED state control pins can have their duty cycles controlled for LED brightness control. Strategic use of the clock signal is necessary to cycle through each column of LEDs within each of the eight layers.