You can offer $180K on a $125K property but I wouldn't and here's why:
1. If the appraisal comes back at anything under $180K you'll be on the hook to cover that cash.
2. Just because your approved up to $180K doesn't mean it fits into your quality of life to spend that much especially if its on an asset that is values at $55K less than that. Have you seen what a mortgage payment will be on $180k at your current interest rate? How much more comfortable are you making that payment than on a $125K mortgage.
3. Have you found out why the seller wants cash only? might have been a typo that they're unaware of or might be some reason that's cheaper to solve than a $55K over asking offer.
4. Do you even know if the property is worth $125K? In my experience if a seller is dead set on anything then their expectations might be unreasonable in other areas of the contract.
5. What are the days on market? That will tell you a lot about what leverage the seller has and how reasonable the asking conditions are.
Hope this helps and feel free to reach out to a local Real Estate Professional or myself if you need help finding one in your area.