At first, I thought this Cornelius might be the same as BK #17710. However, the widow (I supose) Delilah and BK #17710 Cornelius are listed in separate households in the 1860 Census of Cayuga Co., NY. They are right next to each other, though.
From Ronny Bodine:
Cornelius Bodine lived in Niles, Cayuga County in June 1850. His family comprised Delilah 39, Mary Ann 17, Sally 15, Abram 9, William 7 and Francis, 11 months. In June 1860, Delila Bodine 51, was now widowed and living with her children in Niles. The family now comprised Abraham M. 18, William D. 15 and Franklin M. 12. In June 1870, Delilah Bodine, aged 60, lived in the household of her son Abraham in Niles. Cornelius Bodine was buried in Selover Cemetery, Niles, Cayuga County. His grave marker states he died 20 Jan 1860 aged 54 years, 9 months, 4 days (=16 April 1805).