The rest of the verse might be informative

Son giunchi che piegano le spade vendute: già l'Aquila d'Austria le penne ha perdute. Il sangue d'Italia, il sangue Polacco, bevé, col cosacco, ma il cor le bruciò.

For which Wiki gives the translation:

Mercenary swords, they're feeble reeds. The Austrian eagle Has already lost its plumes. The blood of Italy and the Polish blood It drank, along with the Cossack, But it burned its heart.

The "Austrian eagle" can be a reference to the Austro-Hungarian Empire, or possibly to the Holy Roman Empire, both of which came into conflict with, captured, and ruled parts of Italy, Poland, and Russia. Given the reference to Cossacks and the date of Italian unification, it's certainly the former. Thus, the verse is simply talking about others who resisted a mutual enemy.

EDIT: There is some discussion about this verse as a reference to the partition of Poland between the A-HE and Russia, and the link between the struggle for Polish and Italian independence. This is certainly grammatically possible (if ambiguous). This wouldn't explain why Russia was drinking Italian blood, though, so I remain unconvinced.

Italy is also referenced in the Polish anthem

' March, march, Dąbrowski, To Poland from the Italian land.'

He was a military general and after the third partitioning of Poland, he advocated for Polish independence abroad especially in Italy. He founded the Polish Legions in Italy serving under Napoleon since 1797.

Both nations were struggling for independence at the time and somehow managed to get themselves into each others anthems. I'm no expert on that time period , I'm sure there is a better reason for why :)