Hi Paul,
2 litres in 3 weeks is a lot of coolant, and what do you mean burnt up? In the cylinders? That would not be possible (in my opinion).
My trouble shooting suggestion (with extra care of course), is to top up the coolant when the engine is cold. Get the engine up to temperature (90degrees) with the bonnet open. Because the coolant system is under pressure and at temperature, you should be able to see 'leaks' or 'steam'. You may want a second person to rev the engine as the water pump
If you have an undertray, possibly remove that, as that could be catching the coolant?
Again, be careful.
Thanks, Joe