What is the theme of The American Soldier and provide examples and why you think that

Do you mean the poem Memory of the Brave Americans?

No the poem goes like this

Deep in a vale, a stranger now to arms,
Too poor to shine in courts, too proud to beg,
He, who once warred on Saratoga’s plains,
Sits musing o’er his scars, and wooden leg.

Remembering still the toil of former days,
To other hands he sees his earnings paid;--
They share the due reward—he feeds on praise.
Lost in the abyss of want, misfortune’s shade.

Far, far from domes where splendid tapers glare,
‘Tis his from dear bought peace no wealth to win,
Removed alike from courtly cringing ‘squires,
The great-man’s Levee, and the proud man’s grin.

Sold are those arms which once on Britons blazed,
When, flushed with conquest, to the charge they came;
That power repelled, and Freedom’s fabrick raised,
She leaves her soldier—famine and a name!