In my review here:
https://www.head-fi.org/showcase/burson-audio-fun.23238/reviews?page=2#review-20722 I was able to get some spikes coming from 50Hz mains and 2nd and 3rd harmonics...etc., but all are below -100dB, so definitely inaudible. I've also test FUN with 16 Ohms IEMs (100dB sensitivity) and heard no hum at all. Would you mind taking a RMAA and ARTA test to see exactly what's the frequency FUN is throwing on the headphone-out plug?
Meanwhile, I'll try to replicate your sort of defect on my FUN, but not sure I'll be able to. However, I'll use my scope and measure the +/-17V rails, just in case I can spot some strange spikes.
Technically, 50/60Hz should not be there, unless there's a ground issues (polluting ground or ground loop) or it gets induced by the surrounding cables. The MCSP works way above the audible range (>150 KHz) and even some of the lower harmonics might, hypothetically, get injected into the audible band, it will never hit the 50/60Hz noise, instead it will be somewhere between 10-20KHz (if any!). So RMAA and ARTA might help here, but please do a loopback first, then measure the FUN, so we can compare the hum noise induced from the surroundings with the noise from FUN's headphones-out.
Signal/Noise Ratio (50 Hz hum nose is lower then -102 dB)
I sill do again this above test, loopback vs. FUN, just to see if I can spot same issue on mine, after playing a lot with POWER-ON and POWER-OFF, then plug/unplug the headphones, like some said here that might "help" in getting the defect to manifest.