Most small cakes take between 15 to 30 minutes to bake and cook all the way through but some other cakes that are larger can take 40 minutes.
Just make sure to check the cake every 15 to 20 minutes and you can see if the cake is cooked through by sticking a fork or toothpick in the cake and if it comes out clean it's cooked.
If the cake is not cooked all the way in the middle then if it has already cooled down there's nothing you can do really to get it to cook all the way through but you might be able to cover it with some tinfoil and put it back in the oven for another 10 to 15 minutes and it should cook some more.
If it doesn't the cake is not gonna harm you if it's not all the way cooked though.
You can safely eat undercooked cake and it will not harm you although it won't be as good as a fully cooked and baked cake.
Small cakes take between 15 to 30 minutes to bake and cook all the way and be ready to eat but some larger cakes can take as long as 40 minutes.
Once you remove the cake from the oven and allow it to cool down it cannot be baked any further as it will not rise anymore or bake anymore.
You can stick a toothpick or fork into the middle of the cake and if it comes out clean then the cake is done and ready to serve.
If not allow the cake to bake another 5 or 10 minutes and then check it again.
There's nothing in the undercooked cake that will make you sick as I used to eat cake mix off the spoon as a kid and still do and nothing bad has happened to me.