This is a step by step explanation of how to build a 5x5 LED cube using an arduino. I did this project for my undergraduate electronics class and it took me about 2 weeks to complete.
Note: Apparently, some of the links for the supplies and code aren't working, if you need them send me an email at firstname.lastname@example.org.
You can find a video of the working LED cube on youtube here:
And here's another: