I'm thinking of building a 24x24x24 cube (13,000 led's)
Have you any idea of the engineering challenge that represents?
Power supply current, decoupling and refresh rate!
but I'm worried that if I control 1 led of the cube at a time the multiplexing won't be fast enough and will flicker
Well I think flicker is the least of it, if you refresh at a ratio of 1 : 13000 then it will be so dim you will have a job seeing it.
so only 576 leds on each level would be multiplexed ?
So you think reducing it to a 1 : 576 ratio will be better?
I use a 1:4 ratio and find that is enough although you could probably push it to a 1:16 ratio.