Inspired by the following xkcd:
This is just a plain ripoff of http://chiliahedron.com/ballroom/, but in metric units, instead of imperial ones. Seriously, there are three countries left which still use imperial units: Liberia, Burma and the United States of America. Please get a grip and try to cooperate with the rest of the world.
Added bonus: Validating, plain XHTML.
The suggestions given below are just that--feel free to enter nonsensical values for fun and profit. Feedback can be directed to relsqui on the xkcd forum or IRC channel, or relsqui(at)chiliahedron(dot)com.
The theoretical best possible packing density is about 74%, and the theoretical worst (in a space whose dimensions are multiples of a ball's diameter) is about 60% before you stop actually filling the space or start ignoring gravity. Don't believe me? Figure it out yourself.
I recommend excluding bathrooms for sanitary reasons.
If you don't have screen windows, you probably want to stay under sill level … or get screen windows.