I have seen in many bulletin boards that a pilot is supposed to report upon entry into a holding position. I can find that reporting nowhere in the regulations . I can find in the regulations where a pilot must report leaving a hold at expected clearance time, and at that time he is supposed to report time, altitude, and position, and the fact that he is leaving the holding position. Where in the regs does it show that you must report upon hold entry?
So, this is found in the AIM, para 5-3-3 (a)(1)(f) (PDF), assuming you're asking about FAA regulations.
5-3-3. Additional Reports
a. The following reports should be made to ATC or FSS facilities without a specific ATC request:
1. At all times.
(f) The time and altitude or flight level upon reaching a holding fix or point to which cleared.
(g) When leaving any assigned holding fix or point.
Now, the AIM is not regulatory. It uses terminology like "should" instead of "shall", which lawyers will happily jump on, and it in fact says this about itself:
This publication, while not regulatory, provides information which reflects examples of operating techniques and procedures which may be requirements in other federal publications or regulations. It is made available solely to assist pilots in executing their responsibilities required by other publications.
AIM guidance is to report arrival and departure of a hold. Talking with controllers, they don't want to hear the reports, especially when things are busy, in a radar environment. But the AIM doesn't say that.
If you are in a non-radar environment, you must report arrival and departure from the hold. If you are in a radar environment, most controllers in the US do not want a report, but the AIM does not provide that guidance.
I always report entering a hold, except when practicing VFR holds in a radar environment.
As far as I know, there is no definition of what "established in the hold" means.
To address your specific question, I am unaware of where in 14 CFR hold entry reporting is mandated. However, much of the "rules" (really policy) about IFR flight are in the Instrument Flying Handbook and to a lesser degree, the AIM. And in my experience, ATC may ask for a report upon entering a hold.