Hugh was the son of Jackson F. Box and Elizabeth E. Baldwin. Though census records are sometimes rather inaccurate, Hugh's birth year appears to have been late 1848 or early 1849 and would not have been much older than 15 or 16 when he enlisted in the 16th Regiment Cavalry. No burial record has been found for Hugh in Lawrence Co., Missouri; it's most likely he was buried in the Soldiers' Lot of Woodland Cemetery at Mound City, Kansas, a few miles southwest of the Mine Creek Battlefield. I believe he may be an unidentified soldier with a tombstone marked U. S. Soldier.

Hugh L. Box, 18, Enlisted July 21st, 1864 in Dade Co., Missouri as a Private in Co A 16th Missouri Cavalry (Captain Robert M. Hayter), and was mustered in on August 17, 1864. Hugh was killed in action at the "Osage Battle." [Missouri State Archives]
Note: The "Osage Battle" was the Battle of Mine Creek, Little Osage River, 2.5 miles southwest of Pleasanton, Kansas.
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~Linn County Historical Society~
Soldiers' Lot is located in the southwest corner of Mound City's Woodland Cemetery. It was established as a burial site for Union Soldiers. The first interments consisted of 30 Union soldiers killed in the Battles of Mine Creek and Marais des Cygnes in 1864. The site is managed by the US Department of Veterans Affairs.

The first soldiers were re-interred there in 1867. On the 25th Anniversary of the Battle of Mine Creek a ceremony was held to dedicate a monument which still stands majestic watch over some fifty graves. Those buried there include James Montgomery, Jayhawker chieftain; James Findlay Harrison, grandson of President William Harrison; Lt. Curtis, the only Union officer killed at the Battle of Mine Creek; and 17 unknown soldiers.

~Woodland Cemetery, Mound City, Linn Co., Kansas~
The Mound City Soldiers' Lot is located in Lots 262 and 263 of Woodland Cemetery at Mound City, Kansas, which set aside the area for the burial of soldiers. The first interments consisted of 30 Union soldiers killed in the Battles of Mine Creek and Marais des Cygnes in 1864.
[http://www.cem.va.gov/cems/lots/moundcity.asp]

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16th Regiment Cavalry

Organized at Springfield, Mo., November 1, 1863, from 6th Regiment Enrolled Militia. Attached to District of Southwest Missouri, Dept. Missouri, to April, 1865, and to District of North Missouri, Dept. Missouri, to July, 1865.

SERVICE.-- Scout and patrol duty in District of Southeastern Missouri until April, 1865, and in North Missouri until July. Actions in Wright County July 22, 1864; Dallas County September 19; Booneville October 9-12; Big Blue or State Line October 22. Engagement at the Marmiton, or Battle of Chariot, October 25. Mine Creek, Little Osage River, Marias Des Cygnes, October 25...

Lost during service 1 Officer and 12 Enlisted men killed and mortally wounded and 1 Officer and 31 Enlisted men by disease. Total 45.
[http://www.civilwararchive.com/Unreghst/unmocav2.htm#16th]
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Battle of Mine Creek - October 25, 1864
Linn County, Kansas - Union victory

The Battle of Mine Creek, also known as the Battle of the Osage, was a battle that occurred on October 25, 1864 in Kansas as part of Price's Raid during the American Civil War. In one of the largest cavalry engagements of the war, two divisions of Major General Sterling Price's Army of Missouri were routed by two Federal brigades under the command of Colonels Frederick Benteen and John Finis Philips. This battle was the second of three fought between Price and the Federals on this day; the first had been earlier that morning at Marais des Cygnes a few miles away, while the third would be fought a few hours later at the nearby Marmiton River. Although vastly outnumbered, Union forces won all three engagements, forcing Price out of Kansas and sealing the fate of his disastrous Missouri campaign. [Wikipedia, the free encyclopedia]