Dell Precision T3600 8hpgt motherboard

No, the Precision T3600 does not support Xeon E5-2676 v4 processor.

The supported CPU are Intel Xeon processor E5-1600 or E5-2600 Sandy Bridge family. 

https://i.dell.com/sites/csdocuments/Shared-Content_data-Sheets_Documents/en/Dell_Precision_T3600_Spec_Sheet.pdf

@치노 데 오로

Is E5-2690 possible?

Yes, E5-2690 is Sandy Bridge family and is compatible.

https://www.intel.com/content/www/us/en/products/sku/64596/intel-xeon-processor-e52690-20m-cache-2-90-ghz-8-00-gts-intel-qpi/specifications.html

@치노 데 오로 

Thank you for your kind reply.
Finally, I am curious whether versions such as v2, v3, and v4 of the E5-2690 product line are available.

Yes, the newer versions of E5-2690 were made available for newer workstation products.  Unfortunately, they are not backward compatible and not supported on the T3600.