Everyone at one time or another hums to some tune with the song in their head.
Is it normal when a 8 year old does it constantly? As in, nearly every day, sometimes for hours on end (not necessarily same tune). During play. Or quiet time. Or homework. Or even food. Almost never actually sings them.
As an adult who does the same thing, I don't think it's anything to worry about. If they aren't already involved in playing a musical instrument or some type of singing outlet you could find a local option to help them get the music out. I know in my case it's that I really love music and find myself thinking about songs I enjoy or sometimes am noodling a new tune for a song I'm writing. If the current behavior is distracting it's okay as well to tell them you'd rather they not hum in certain situations. That's how they'll learn when it's appropriate and when it's not.
My 7 year old was recently diagnosed with ADD and this was actually a question on his assessment and yes, he hums all the time! He has done this since he could talk and honestly, it drives me up the wall but according to his psychiatrist, it is a way for kids with ADD to keep themselves "busy" and they really do not even realize they are doing it.
You would have to qualify the definition of normal to get an appropriate answer but I'll go ahead and assume you are asking based on the majority of other children. I would say this is normal. I used to hum all the time. Sometimes I would sing too, but mostly hum but then I started playing guitar. While sometimes I still hum, when I am feeling "musical" I usually go grab my acoustic and play for a bit.
Also, it's not uncommon for someone to get a song stuck in their head. I despise having a song stuck in my head because otherwise, once again, I'll start to hum it without even realizing it. My cure for that is to put the song on repeat until I am absolutely sick of it.
In summary, either get the kid an instrument, ignore it, or find out which song is stuck in their head so they can quickly purge it and you can go back to enjoying meal time.
Whether it's normal is almost beside the point for me. My 14-year-old does this incessantly, and it is occasionally really difficult for me to deal with. She usually doesn't do it very loudly, but something about the timbre of her voice makes it cut through -- it's impossible to ignore even when she's doing it quietly.
Occasionally, she does it loudly, and then I feel totally justified in telling her to stop. But it appears to be a compulsion for her because sometimes we'll be right next to each other (e.g. watching a movie), and she'll stop after I ask her to, but 20 seconds later, she starts again. When I call her out, she apologizes. She just doesn't seem to realize she's doing it.
I actually have songs going through my head almost constantly, so I'm not surprised that she does. The difference is that I was never compelled to sing them aloud -- I just "play" them in my head. The only thing close to a solution I have is to ask her to do the same (i.e., just imagine the melody in her head) when it starts to feel like water torture to me.
