As the designer of the world, the Dungeon Master determines volumes and dimensions of objects.
“1 cubic foot” is not ambiguous, it’s just a volume of undefined dimensions. What is ambiguous is the volume of objects the Dungeon Master is describing, and so if it becomes relevant, the Dungeon Master needs to make a ruling on the volume of the object. As a mathematician, I generally try to avoid math when I DM, I do enough of it at my job, and more importantly, calculating volumes while we’re trying to play the game is generally a waste of time.
For something like this, I’d just make a decision and move on, just to keep the game moving, and I highly recommend everyone else do the same. And that’s the beauty of being the DM: you don’t have to do math because you can just make it up and it becomes true in your world.
The way I make rulings like this is rather inelegant: I imagine the object in my head and make a guess. I’ve just never encountered a player that much cared about whether or not their prestidigitation worked based on the size of the object. To be clear, in every campaign I have run I’ve had characters taking prestidigitation, and I’ve had to rule on this before, but every time I’ve said “nah that’s too big”, the player says “alright” and moves on. The stakes are just never high enough to care much. If I encountered a scenario with exceedingly high stakes and the outcome depended on prestidigitation working, and the volume of the object was the deciding factor, then I might consider doing the math.