Following whose inauguration was the first inaugural ball in Washington, DC, held?
The first inaugural ball was held in 1809 following the inauguration of James Madison.
You can see two pages of the Senate tabulation of electoral college results from the 1808 election
[Records of the US Senate, RG 46 (10A-H2), (83A-L1, Box 414)]
Page 1 [35K JPEG]
Page 2 [8K JPEG]
One of the functions of the National Archives is the administration of the Electoral College.