Those aren't multiplexing chips. Those are just chips to give you more outputs than your arduino has.
The multiplexing is just done on the microcontroller. But it depends on how you are wiring the leds. You can wire the cube to use less digital outputs, but you'll end up with a less bright leds.
You could use no multiplexing. That way the leds are lid with a 100% duty cycle. But for that you'd need 512 outputs.
You can choose to light up only one level at a time. That way you only need 72 outputs (64 for the leds, and 8 for selecting the level). This is a form of multiplexing. Since only one level is lid at a time, the leds have a duty cycle of 12.5%. Please note that because of the way humans perceive light, it will look more like 1/3rd the brightness, instead of 1/8th (so that's great). Also note that since you only need one level to be on at a time, some people prefer to use a decade counter IC for that.
You could also choose to only light one row at a time. That way you only need 24 outputs (8 for the leds, 8 to select which row, 8 to select which level). But you'd need some additional circuitry to combine row- and level-selection.
There are specialized multiplexing IC, but those only support rows and colums (not level). So you need 1 chip for each level, and more problematically you need to run 8-row and 8-culumn wires for each level to the bottom. That's quite a bit of wire, which might ruin the aesthetics of the cube.
In short. There are quite a few ways of making a 8x8x8 cube. I'd suggest finding a well documented build from someone else that you like and follow that.
Quite a bit of information. I hope it's of help. If you have any more question feel free to ask.