I think this would depend on which ship you are sailing on. You should be able to telephone your cruise holiday provider and enquire about the formal nights directly. We have found that as a rule typically for a 1 week holiday, there are 2 formal nights, at the start and end of the cruise respectively. Thery are all part of the fun and experience of the cruise. You can be as dressed-up as you wish really. Long gown/tuxedos or smart dress/dark suits or ladies evening
trouser suits. The inbetween nights dress as though you were going out to dinner athome to a nicer restaurant. I love it and enjoy dressing up in my posh frocks, as i call them, with my bling on and my hair having been done in the salon onboard, but it doesn't have to be like that and usually there is the option to eat elsewhere, in one of the buffets or grills for example and then you can just go as you are. There is the option of room service to eat in your cabin as well. But don't be put off by tales of "dressing up to go to the ball" style eating there really is a mix of clothing styles, i think maybe not jeans and jeans style casualness,t.shirts etc to dine in in the evening meal restaurants as a rule. Look up your chosen ship on this site and have a peek at the 'photos and see what people are wearing whilst eating and maybe check out your brochure, if you have one,or google the ships name and and when it pops up query clothing required while dining onboard,that's what i did for all sorts of queries and it really helped. There are casual-style cruising ships where you can wear what you want, Ocean Village is one, where you don't dress up unless you choose to, just google Casual Style Cruising and options will pop up for you to view. Hope this helps and that you enjoy your cruise.