This looks like the Packham family in 1870, I do not find them in the 1860 census.

Although John is said to have been born in Ohio, it appears that he actually was born in North Carolina.

As father Albany joined the 34th Ohio July 26, 1861, they may well have been in Georgia earlier in the year, or perhaps John was at school in Georgia

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Albany Packham in the 1870 United States Federal Census

Name: Albany Packham
Age in 1870: 46
Birth Year: abt 1824
Birthplace: England
Home in 1870: Prestonsville, Carroll, Kentucky
Race: White
Gender: Male
Post Office: Prestonville

Household Members:
Name Age
Albany Packham 46 Ret. Merchant
Athar Packham 40
John Packham 21 Distiller born in Ohio
Allen Packham 15 Attg. School -do-
Flora Packham 12
Carrie Packham 10
Frederick Packham 3

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Although the three reenactors have chosen to join a Confederate unit that was based in North Carolina, in an ironic twist, they share an ancestor who was born in the South but became a soldier in the Union army. John W. Packham, Fowler’s great- great-grandfather, was born in Fayetteville, N.C., but left home to join the 34th Ohio Unit. He was even younger than Jeremy when he made the decision to enlist.
“He lied about his age, he was not yet 13, and was supposed to be 16,” said Fowler.
http://bcwrt.nalweb.net/Pages_07-06.pdf

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Photograph, “J. W. Packham, Fifer and Regimental Marker of 34th Ohio Zouaves,” Frank Leslie’s Illustrated Newspaper, November 8, 1862. West Virginia State Archives
http://www.wvculture.org/history/sesquicentennial/photos1862.html

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Albany Packham
Residence was not listed;
Enlisted on 7/26/1861 as a Comm Sergeant.
On 9/12/1861 he mustered into "K" Co. OH 34th Infantry