I usually have no problem with the baking part of making cakes (it's the decorating that defies me!); and for some reason, when I make cake in my 10" Magic Line square pan I have major issues with the center falling. Normally, I have issue with it rising, which is ok, because I like to have a bit of the top to taste to ensure quality (and I enjoy seeing inches added to my hips 
). I have tried overbaking and underbaking with the same results. I do drop my pans and level the batter so I'm not sure what's happening. I know it has to do with size because I have no problem with the 6 and 8" versions of the same pan. What gives?
For the heating core - you will need to treat it as you do your pan if you use pan grease, Pam or whatever (be sure to treat the inside as well). Put some of your batter inside the core then place it in the center of you pan and fill as usual. After the cake is baked I immediately take my core out and put it into the hole in my cake and let them cool together. Before you flip you cake out of the pan just level off the core.
HTH
Melissa
Theres a list online that tells you probable solutions for baking online thought it may help. 
Coarse grain & sunken center
Oven too cold (baked too slowly). Preheat oven for about 20 minutes.
Sugar and fat under-creamed. Follow my Creaming Steps.
Batter undermixed
Too much baking powder.
Not enough liquid
Too much flour
Used all-purpose flour instead of cake flour.
Careless or poor depositing in the pans.
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