How can I soak cake in cheese?
The thing is mascarpone doesn't really have much flavour. If you dilute it and a little soaks in, you won't be able to taste it at all. The much runnier liquid used in lemon drizzle cake doesn't soak in very far. Maybe you don't want too much cheese flavour, but something like mascarpone or ricotta would be better as a filling or topping than trying to flavour the cake itself 

For a real cheese flavour I reckon you'd be better off mixing cheese in before baking. I have tasted a dark chocolate and blue cheese cake. Delicious and very rich. The concept came from Heston Blumenthal.