It is never recommended to house such different species together in a cage. Budgies (in the parrot family) and finches which are softbills, are too different in temperament, behavior, lifestyle, not to mention the obvious size difference. I’ve seen certain finch species with gentle parrots such as budgies and cockatiels in a larger mixed aviary, but that is a different thing all together than a cage.
Although I have seen people with 3 budgies who live together harmoniously, it is taking a great risk once the birds are mature. When their hormones kick in, two males will have a high chance of fighting over a lone female. Then with two females and one male, the dominant female or the pair can become aggressive to the other one. It’s generally not recommended. I’ve known someone who kept 3 together and it worked out with their individual personalities, but that is not always the norm.
A good size cage that we recommended for one budgie is 18x18x30 inches minimum. 46x46x76 centimeters. For example this: https://express.google.com/product/1...235874_5643243
Of course bigger is even better.
A nice size for 2 budgies, is a standard sized flight cage. The dimensions are around the same at the previous one except it is much taller at about 91cm high. Here is an example of such a flight cage: https://www.houzz.com/product/592187...l-pet-supplies
If you can’t find these items where you live, then just make sure the size is not too small. If you are uncertain, please take a photo and show us