Much less than you'd think if you are willing to go with 6TB only. The 128GB modules are awfully expensive but the other day I saw 64GB modules at $600 https://memory.net/product/s26361-f3843-e618-fujitsu-1x-64gb... here. So that's ~39K for 6TB of RAM. The relevant Supermicro server (4048B-TR4FT) with four E7 CPUs is ~14K http://www.thinkmate.com/system/superserver-4048b-tr4ft comes with 32 4GB modules which is a waste but oh well, it's a very small loss compared what it would cost to buy 6TB at a server seller like this. So you are looking ~53K for the server, CPU, 6TB RAM, you will need a little storage as well, so perhaps ~60K for a 6TB 4U server. In closing, let me remind you that a mere two decades ago, Microsoft launched the Terraserver which was a demonstration of a server with a terabyte of storage and it was very big news. Now we are here with a machine at the price of an ordinary F-150 truck or so which can hold the 5TB uncompressed data of the Terraserver in RAM.
Possible on consumer chips, or possible? Because Intel and AMD have both shipped 6+ core parts for some time now, just usually not targeting the consumer segment...
IIRC when asked, Intel folks say they haven't make a consumer 6+ core part because there's little benefit/demand, but I can't find a citation for that. [1] is a nice discussion about why we haven't gotten more than 4 cores in consumer parts yet, though.