How to determine finch gender by looks, beak color, and singing?

When zebra finches are all white it is sometimes hard to tell if they are male or female as they won't have the characteristic cheek markings, beak coloration or tail patterns. The two pictured look like they could possibly both be female, but it is hard to tell due to the distance from the camera and the lack of markings present (males will sometimes still have darker cheek areas, a stripe on the cheek, or a darker red beak). Males will also sing almost constantly that sounds quite different than regular chirping, and will also "tail waggle" when they are wanting to/attempting to mate with a female. If none of your birds are doing this, it is possible they are all female. Both males and females will show interest in nests and will go in them to sleep at night even if they aren't raising babies. If one is being left out, you can add in another nest or sleeping area to see if it helps.

Gouldian finches are sexually dimorphic (meaning the color patterns are different between the male and female birds) so if your birds are the ones in these photos or they look identical to them, then it would appear you have a male and a female bird. Both sexes can make noises/calls, so perhaps you are hearing both birds making noises, though the males are the ones that have what people call a "song".

Sexing male and female Society Finches is extremely difficult. Mating behavior will give you a clue as to the sexes of your finches. Males sing, and when next to the female will often stretch their necks and fluff their feathers. Both sexes will make chirping sounds. the only way to find out the sex of a Bengalese Finch is to have a DNA test done (this is done in special labs with 1 drop of blood from the bird).

Both sexes can sing but male are usually more vocal. Some of the breeds have distinguishing external characteristics like brighter cheek patches (males) or horizontal bars on tail and primary feathers (once sexually mature). A veterinary visit can take a small blood sample to determine sex. Good luck.

Ideally, the more space the better, and three birds should have a flight cage that is big enough for them to fly back and forth horizontally in (finches tend to like horizontal rather than vertical cages). You also want to make sure each bird has their own access to food, water, and bedding areas, with dividers such as perches or toys to break up the space and prevent fighting over territory. If you do introduce a new bird, make sure to keep him separated for a week first to prevent the spread of any illness, and to make sure he is healthy enough to be added to the flock before doing so.

If they are at least 12 months of age, you can determine gender by looking at the color of the cere (nose). In males, the cere is a blue color. In females, it is tan/brown. If they are younger, you will need to wait or you can have them sexed by DNA using blood or feather samples.

Going by cere color, I would agree with your assessment of gender. If you want to know definitively, you can have them sexed by submitting DNA samples (feathers or blood) on each bird. Your veterinarian can do this for you. An experienced avian veterinarian can also sex the surgically.