Does it have 3 lunar LED's?
From a search, I found a thread for Biocube that says "The stock Biocube power supply is rated as DC 4.0v 100mA output. It currently powers 3 LEDs."
So, it should be as easy as finding a power supply that has that output AND the right plug shape with polarity.
I did find a power supply for a "Remington Shaver Charger Ud-0401" that has that output, with a center positive plug. Not sure if the plug is the same size, probably not. But for $12 on ebay, may be worth it.
Otherwise, I'd check grainger or mouser for something universal where you can pick your plug. most of those go for $15-20, which might be the price of a new lunar LED module and supply anyway.
Full disclosure, I don't have a biocube, so I can't check for myself. Hope this helps, maybe someone else will weigh in.