You can generally visually sex cockatiels, but if you're not sure it doesn't hurt to get them DNA sexed. Depending on where you live, it can cost as little as $15 per bird. But, if they are male and female, it doesn't necessarily mean that the male is properly fertilizing the female's eggs during mating. He could be poorly positioned during the process. If he is successful, which you'd only know with a second cockatiel female introduced to him that he'd want to mate with, then it's also possible that the female cannot provide the proper nutrients for producing sufficient yolk for the developing embryos since she's laying so many. Her diet is pretty key for that.
There's also a good possibility that because she has so many, she isn't sitting on them properly and can't incubate them the way she should. Poor temperatures result in no development. If you've seen them mating, then those are the only possibilities I can think of. If you haven't actually seen them mating, it's very possible your female is just laying the eggs because she feels that the conditions are right.