I've read some online post on shift registers and find out each shift resigster like 74HC164N controls 8 leds, while 3 pins are used on arduino uno. so if i build a 8x8x8 led cube, that would require a total of 72 pins to control them. in this case, i can only use up to 4 shift registers because arduino uno have to give 3 pins to each shiftregister. and 4X8 is only 32 ouputs.
Yes, an Arduino Uno can do it.
There's hundreds of tutorials on the web about how to make LED cubes, try reading a few to get some ideas....