These two are very popular songs from the US Civila War used for both marching and singing - one from the Union Side and the other Confederate. It's important to note that the second one, Bonnie Blue Flag, was as popular, if not more so, than Dixie at the time. It's also a bit of US Army lore that a Union Soldier once rallied his unit during a retreat by singing the refrain from the Battle Cry of Freedom.

Battle Cry of Freedom

So we're springing to the call from the east and from the west,
Shouting the battle cry of freedom.
And we'll hurl the rebel crew from the land we love the best,
Shouting the battle cry of freedom.

The Union forever,
Hurrah, boys, hurrah!
Down with the traitor,
Up with the star!
While we rally 'round the flag, boys, rally once again,
Shouting the battle cry of freedom.

We are springing to the call of our brothers gone before,
Shouting the battle cry of freedom.
And we'll fill the vacant ranks with a million freemen more,
Shouting the battle cry of freedom.

The Union forever,
Hurrah, boys, hurrah!
Down with the traitor,
Up with the star!
While we rally 'round the flag, boys, rally once again,
Shouting the battle cry of freedom.

We will welcome to our numbers the loyal, true and brave!
Shouting the battle cry of freedom.
And although he may be poor, not a man shall be a slave!
Shouting the battle cry of freedom!

The Union forever,
Hurrah, boys, hurrah!
Down with the traitor,
Up with the star!
While we rally 'round the flag, boys, rally once again,
Shouting the battle cry of freedom.

Bonnie Blue Flag

We are a brand of brothers and native to the soil,
Fighting for the property we won by honest toil,
And when our rights were threatened, we rose from near and far,
Hoorah for the Bonnie Blue Flag that bears a single star.

Hoorah, hoorah for Southern rights, hoorah,
Hoorah for the Bonnie Blue Flag that bears a single star.

First gallant South Carolina nobly made the stand,
Then came Alabama and took her by the hand,
Next quickly Mississippi, Georgia, and Florida,
All raised on high the Bonnie Blue Flag that bears a single star.

Hoorah, hoorah for Southern rights, hoorah,
Hoorah for the Bonnie Blue Flag that bears a single star.

And here's to brave Virginia, the old dominion state,
With the young Confederacy at length has linked her fate,
Impelled by her example now other states prepare,
To hoist on high the Bonnie Blue Flag that bears a single star.

Hoorah, hoorah for Southern rights, hoorah,
Hoorah for the Bonnie Blue Flag that bears a single star.

Then cheer boys, cheer and raise a joyous shout,
For Arkansas and North Carolina now have both gone out,
And let another rousing cheer for Tennessee be given,
The single star, the Bonnie Blue Flag, has grown to be eleven.

Hoorah, hoorah for Southern rights, hoorah,
Hoorah for the Bonnie Blue Flag that bears a single star.

That's interesting, where did you did you find that of you can recall?

another one is the unions When Johnny Comes Marching Home