The world's smallest 3x3x3 was designed by Evgeniy Grigoriev, he used to sell a 3D printed kit for building one but it is no loner available, his cube came in at 5.7mm. Tony Fisher used this design but shaved down the pieces slightly to achieve a size of 5.6mm , this is listed in the Guiness Book of World Records as the smallest 3x3x3 cube ever made.
The smallest cube you can buy is the Cubelab 1cm 3x3x3, this is just 10mm in diameter but turns surprisingly well considering its size, I have solved this in 43 seconds which was an unofficial world record at the time but has since been beaten by Kim Roger Høyland-Larsen who solved it in 31.70 seconds!
The Cubelab 1CM 3x3x3 is surprisingly popular so it is clear that there is a market for insanely small cubes, it is difficult to see any other company manufacturing anything significantly smaller though, the cube has to remain stable and be usable.
