Question: Do I need to provide evidence to prove a breach of contract when the breach is admitted?
Answer: Yes evidence is always required. Every claim has two parts to it: proof of liability and proof of damages (actual loss).
The Global News reported a good example of the need to always provide evidence. A decision by the BC Civil Resolution Tribunal issued 23 May 2023 concerned a Claim by Mr Webbe against the 50th Parallel Estate Winery for the return of his damage deposit: https://decisions.civilresolutionbc.ca
Liability was not an issue because Mr Webbe admitted that one of his guests had breached the contract by firing a confetti cannon during his party which was also a rather obvious factual occurrence.
However, evidence of actual loss has to be provided and the Winery failed to provide adequate evidence of actual loss. The winery did provide some invoices to confirm some cleaning had been done but the invoices lacked the detail required to prove the cleaning was directly caused by the confetti and not normal cleaning, especially since the dates of the invoices if not the actual cleaning were some weeks later. Thus the decision was that the Winery had to return most of the damage deposit.
Generally, evidence can be both physical such as documents, and witnesses who have direct knowledge of the relevant events eg saw and or heard personally, not hearsay.
The moral of the story is to provide evidence of everything you want to be believed including specific loss.