It's in the Mammillaria
genus, but I can't offer you any more detail, such as species or variety. There are hundreds of cacti in this genus, and I have a difficult time doing a solid ID just from photos on a computer monitor. I'm sorry about that. Perhaps another of our members can help you.
"Isn't it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too?" - Douglas Adams