In Ramayana is one part of his story and other in Padma Purana. Is there an specific text with the whole history,
Not a specific text dedicated completely but there is a section called Bharagava Charitam from Brahmanda Purana which talks about Parashu Rama. Chapter 22 to Chapter 47 of Upodghata Pada deals with the narrative of Bharagava Rama i.e., Parashu Rama.
This section deals the story before Ramayana. It ends with Parashurama gifting earth to Kashyapa.