Amplifier Hum - Only Amp Connected

I have read many threads on here about various amplifier hum.

I recently bought a used tube amplifier.  When I connected the amp and turned it on, I immediately heard a hum from the mid-range driver of both speakers. The hum is audible even if the pre-amplifier is turned off/muted. In fact, I unplugged all interconnects from the amplifier and still heard a hum when the amp was on. I then unplugged the the interconnects and unplugged everything else in the room from the outlets (turntable, pre-amplifier, TV, and cable box), so that the only thing in the room connected to the wall was the amp. I still hear the hum from the speakers when it is only wall>power cord>amp>speaker cable>speaker.

This has to mean that it is a problem internal to the amp, correct?