Earlier quoted context omitted.
Actually, one liter is _exactly_ a cube 10cm x 10cm x 10cm.
I get nervous about precicsion with this because there's the stuff about raising one cubic cm of water by one celcius uses one joule. But there are a bunch of caveats to that and I can't remember them. But thanks for the information!
So even though the volume of a given mass of water might be temperature dependent because water expands if you heat it, the the volume of a given volume of water will always be exactly equal to that volume of water. Sort of like how a foot is always exactly 12 inches no matter what the weather report says.