8x8x8 multiplexed LED cube with an Arduino Mega 2560

CrossRoads:
Seems to be a logic level part
http://www.irf.com/product-info/datasheets/data/irf9540n.pdf

No, it is most definitely not a logic level part. Rds(on) is quoted at Vgs=10V only. It might just work @ 1.28A, it depends on whether the part you get has a higher or lower than normal gate threshold voltage, whether the 5V supply is a little higher or lower than normal, and on the temperature. Bad choice for this project.