i made one the other day and i used a 50/50 mix of pound cake and box cake, and baked it upside down, let cool some before opening the pan....i hope this helps
The problem I had with it was that the cone thing touched the side of the pan and left a hole. What type of cake did you use? I used a fudge marble and I let it sit for about 10 minutes then opened it on each side to release steam. But I waited about 20 minutes total before actually taking out of the pan!
When I made my mini bear, I did not use the cooking core. I used a regular box chocolate cake mix for the little bear. I have read that on the bigger bear some use a denser cake mix. You have to do a flip flop method on cooling. In other words, after about 10 minutes out of the oven take off one side of the pan and let it cool for about 5 minutes. Then put that side back on, turn it over and take off the other side of the pan to cool. Do this several times. When it is completely cooled, I froze mine then decorated the next day... Hope this helps! 
Pat
You don't HAVE to use a core with the bear, I've done them without.
IF you took the cake out after 20 minutes it wouldn't have been cool and that might have been your problem. You need to leave it in the pan until it's completely cool, leave one side off to allow steam to escape and flip it a couple times.
I've only made it once and I did make it w/ one regular cake mix and one pound cake mix together to get a denser cake. I did let mine cool about 10 min and then laid it on it's side and removed one side of the pan, let cool some more and then took it out all the way.
The heavier cake seemed to help hold the weak spots better. JMHO
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