How do you make a cake with soft fillings baked inside?
I have a few recipes that are made like that, and the general technique is:

1) Fill the cake tin with half of the batter you would use for a cake;
2) Spoon or pipe the required quantity of filling;
3) Fill the tin with the rest of the batter;
4) PROFIT!

It doesn't work with all fillings, considering that you need to have a filling that is heat resistant (buttercream is a no-no) and that doesn't expand when heated (nothing too airy). 

The recipes I have call for brigadeiro (which is a kind of chocolate fudge made with condensed milk, powdered cocoa and butter, previously cooked), dulce de leche, fruit jam and one of them uses a mix of cream cheese, sugar and Bailey's, and all of them work very well.