That will be about a 500-600Watt PSU.
Sound damping does not remove sound, it changes the frequency somewhat. Furthermore, internal temperature will increase in the case - there are less ways the hot air can get out - and that will cause the CPU and GPU coolers to run faster - and more significantly louder! 8-core sounds like a I7 - that CPU will generate a lot of heat and need a strong CPU cooler (I only have an AMD quadcore for comparison).
It's a bit of a difficult situation, really. You might be better off not getting an airtight, super-padded case, but a larger, more open tower enclosure with a fan controller, to adjust them to your needs.
For example my case is rather open so I can turn down the case fans and the internal fans run a lot more quiet because there simply is more air inside.