Cheated on an exam when I was eight years old. Should I tell graduate admissions?
As noted in the comments, actions committed long ago as a child are (and should be) entirely irrelevant to graduate admissions.
It is well understood that children do not have same ability as adults to comprehend the consequences on their actions. As a result, many legal systems wipe a child's record clean of most or all juvenile offenses upon reaching adulthood.
I would thus similarly argue that any academic offense predating your undergraduate education should generally neither be reported nor considered in an application for graduate school.
The accepted answer is absolutely correct, but I'd like to make a point that I don't see anywhere else. Do you personally think that the incident in question has any bearing on your current academic fitness? I'm going to venture a guess that your answer is a solid "No".
Looking at it another way, were the situation reversed, would you care if an applicant to your program cheated once when they were 8 years old? Once again I'm going to have to guess your answer would be "No".
Frankly I bet that nearly everyone has cheated on a test or homework or something in their youth (I know, I know, citation needed). The only way that could have any relevance now if if that one incident became a pattern that followed you throughout your education or other parts of your life. I can personally say that I helped a couple friends cheat on tests in high school, and got caught once, but it never followed me into college because at that point I started taking education seriously and dropped all of my old bad habits like cheating, not studying, etc. When I was young I simply didn't care. As an adult, lack of caring can easily lead straight to unemployment.
This answer is about the US educational system.
While the answer for your particular situation is simple --at the age of eight, for a minor offense, no one will be bothered about this-- I'm going to write a fuller answer to cover possible future questions about this general topic. I will include information about the undergraduate admissions process, because it is better documented, and because it will be useful for comparing and extrapolating.
There are some situations where a student's discipline record could be scrutinized by an admissions officer, but:
Students' discipline history is more interesting to admissions officers at the undergrad level than at the grad level, since undergrad behavior problems are more of a campus issue than grad student behavior problems.
Generally, academic and discipline records prior to 9th grade are washed away with the tide; generally, only high school records are reflected in the high school transcript sent to colleges (see, for example, https://talk.collegeconfidential.com/college-admissions/48282-suspension-in-middle-school.html).
What types of high school discipline records might be a concern for undergrad admissions?
According to an article in Education Week,
At a typical high school, a minor offense might result in you being reprimanded by a teacher or told to sit out in the hallway. Repeated minor offenses, or a slightly more severe offense, might result in a detention or an on-campus or “in-school” suspension.
If you get in trouble and you receive one of these punishments, it’s generally not something that you’ll need to report to colleges. However, if your offense merits more serious consequences, it’s a different story. This might include off-campus suspension, expulsion, or the involvement of law enforcement. If one of these has happened to you, you’ll need to report that on your [undergraduate] college applications.
College Confidential interviewed undergraduate admissions officers for an article about the effect of high school suspensions on college admissions. The take-home messages I took from this article:
If an applicant believes a particular incident will be disclosed as part of an educational application, a separate statement of explanation can be appended to the application.
As the article's introduction states, "There is life after screw-ups, even for elite-college aspirants, but [...] honesty about an infraction--and the lessons learned from it--is always the best policy."
As one of the admissions officers interviewed said, "Colleges understand that students are people (just like admission officers), capable of making mistakes or bad judgments."
In a 2016 study, the Center for Community Alternatives (CCA), a nonprofit organization in New York State, found (see summary, full report):
73% of colleges and universities surveyed request the high school disciplinary record;
89% of those who request it, use it in their decision making;
50% of high schools surveyed disclose disciplinary information to colleges in at least some cases;
63% of high schools surveyed don't have written policies guiding them in disclosure decisions.
(Note for undergraduate applicants who might be reading this post: Under the Family Education Rights and Privacy Act (FERPA), parents of minors, and adult students, have the right to inspect their educational records. One can informally or formally attempt to get certain records expunged. Also, the CCA published a helpful guide in 2013 for handling disclosure of criminal records when applying for college.)
Bottom line:
Administrators at educational institutions are aware that young people's brains are immature, and they know that if they tried to restrict admission to people who have never gotten in any kind of trouble for anything, campuses would be sparsely populated.