A cubic centimeter that weighs forty billion tons sounds like a lot, but it is not much compared to the entire planet. I don't think that the extra mass would be enough to pull the moon into us or anything that dramatic. Though, if it was suspended above your head it may be enough for you to notice it.
There is a real problem in trying to contain something with so much mas and so little volume. It would fall right through any surface that was under it and tear a hole through the earth. Eventually it would come to a stop somewhere in the interior. I don't think that it would make it to the center though. As it got deeper, the downward force would lessen as more of the earths mass is all around it, instead of under it. That, in combination with friction would stop it from shooting back and fourth from one side of the planet to the other.