A NATION ONCE AGAIN, by Thomas Davis, can be seen (by some of us anyway), complete with sheet music and a piano arrangement, in The Spirit of the Nation: Ballads and Songs by the Writers of "The Nation" (Dublin: James Duffy, 1845).

However the tune given there doesn't seem like the tune I'm familiar with. (My sight-reading skills are very shaky, though.)

It also has this footnote, which may clarify the reference to "Three hundred men and three men":

The Three Hundred Greeks who died at Thermopylae (7 Herodotus 202), and the Three Romans who kept the Sublician Bridge (2 Livii 10.)

See Battle of Thermopylae and Horatius Cocles in Wikipedia.