Ah, I see! You’re referring to the famous "sum of three cubes" problem, also known as the Diophantine equation x³ + y³ + z³ = k. This problem has been the subject of much mathematical investigation.

As of my last update in January 2022, solutions have been found for all integers from 1 to 100 except for the number 33. The solution for the number 42 was indeed considered particularly challenging due to its properties, but it was eventually found.

It’s a fascinating problem that has intrigued mathematicians for decades. If there have been any new developments in this area after January 2022, I wouldn’t be aware of them. Thank you for sharing this interesting piece of mathematical history!