It refers to Lord Shri RAM (son of Raja Dashrath) .Why it is so because the sloka clearly state word रामः
Means Just Ram but not Parshuram or any other Ram .Because Lord Ram with his शस्त्र is undefeatable .Even Lord Shri Parshuram has acknowledged it During Goddess Shri Sita swayamvar prasang .
Further In shrimad bhagvatam when lord Brahma worshipped Lord Krishna He urged sloka :
सत्यव्रतं सत्यपरं त्रिसत्यं
सत्यस्ययोनिं निहतं च सत्ये
सत्यस्य सत्यमृतं सत्यनेत्रं,
सत्यात्मकं त्वाँ शरणं प्रपन्नः
He called the Lord as सत्य and everything related to him as सत्य mean Lord himself is सत्य and whatever he says/speaks is सत्य ,So when the Lord says राम then it means just राम but certainly not परशुराम ,otherwise it will be a lie aka असत्य and God never lies .
I know you may argue that Lord Shri Krishna manipulated things as suggested in Mahabharata and all but that is nothing but a fallacy ,Don't get influenced by the narrative made by so called different Dharmic serials and their creators , In the name of creativity they disrespect the dignity and purity of the Lord . Lord never speaks a lie ,Infact whatever he says becomes the ultimate truth because this is what God is all about , the truth and only the Truth . If you want to know the truth then you should read the actual ancient sculptures rather reading it through its interpretations. Jai Shri Krishna !