I discovered this one yesterday. Was facing the street, so I hadn't noticed the flowers. This cactus has never failed to bloom every spring for the last 5 years or so. According to Google Images, this is a Mammillaria zeilmanniana, but it has so many synonyms that maybe I didn't choose the most common one. Everything fits the description and pictures, so let's say it is.
I just noticed that this one already has a fruit, bottom/center of the picture, just above the Asparagus that is growing there. It looks like it's trying to take over the balcony, this one. I removed at least 7 yesterday alone. It's not that we don't like it, but one is more than enough. They tend to "eat" the soil and at least on one occasion one of them has broken the pot. So they have to be kept under control!