What does the tap water taste like?
Is the tray they go into clean?
Try taking some old fashioned plastic cube trays ($1.65 at supermarket) and fill them with bottled water and leave them in the fridge for the same period of time. If it is the water then the bottled water tray cubes will taste fine after a few days and the maker ones won't. If it is the contents of the fridge then they will both taste bad. Clean EVERYTHING out of the freezer and the fridge, top and bottom. Clean every surface. Don't put any food in the fridge that isn't sealed tightly, top and bottom. Try test again.
Other things: The plastic or copper flex line water pipe that connects the fridge to the wall might be contaminated, as might the internal plumbing or there is something polluting the maker itself. My guess is that you have smelly onions in the bottom of your fridge - clean your darned fridge you pig <joke>
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