Here's two census records from Cherry Creek, New York 1930 which suggests a 1922 birthdate
"United States Census, 1930", database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:X7HJ-59V : 8 December 2015), Paul R Gross in entry for George J Gross, 1930.
United States Census, 1940," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:KQLC-GMD : 17 May 2014), Paul Gross in household of George Gross, Cherry Creek Town, Chautauqua, New York, United States; citing enumeration district (ED) 7-15, sheet 1A, family 7, NARA digital publication T627 (Washington, D.C.: National Archives and Records Administration, 2012), roll 2509.
Here's a death record consistent with the above that suggests a DOB of August 25, 1921.
United States Social Security Death Index," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:JKTC-N2Q : 20 May 2014), Paul R Gross, 11 Mar 1994; citing U.S. Social Security Administration, Death Master File, database (Alexandria, Virginia: National Technical Information Service, ongoing).
Is this the individual you were looking for?
Since the father and mother were in Cherry Creek both before and after Paul Robert was born, I would guess that is the birthplace.
"United States Census, 1920," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MJKR-QM4 : 14 December 2015), George Gross, Cheny Creek, Chautauqua, New York, United States; citing sheet 13A, NARA microfilm publication T625 (Washington D.C.: National Archives and Records Administration, n.d.); FHL microfilm 1,821,090.
