I have been doing some searching around the records on Ancestry and I see where you are getting Groton, Tompkins Co. as his place that he died per the Social Security Death Index. I have found two sources US Dept.Veterans Affairs that note that date of death is 24 Feb 1979. Also, he enlisted 27 Nov.1943 in Onondaga County, NY and was released 26 Feb. 1946.per US World War II Enlistment Records. He was married at the time of his enlistment. I found on the website Fultonhistory.com that he married Ethel Hall Sept 1940. There is a photo of Ethel with the write up.
The SSDI also had that Claude's birthday was Aug 22 1912.Other members of Ancestry who are researching Claude Cole with this birthdate and date of death note that he died in Onondaga County, NY. You might want to connect to them thru Ancestry or check the Syracuse Herald-American or Syracuse Post-Standard newspaper archives for the Obituary. Sometimes, residents of the Groton Nursing Home in Groton, Tompkins Co. NY died there, but were not really from the Groton area and there was no obituary put in the Groton paper by family.
Looks like there are census records for the Syracuse area Onondaga County, NY for Claude and there are other members who have the tree with Helen and Daniel, parents Charles Luther Cole and Katherine Frey Cole. Hope this helps. Karen.