My Goodman Heat Pump since new has made a loud hum or cycling noise outside from the compressor unit. This noise lasts about 10-20 seconds and then stops. It also makes this same noise when the units shuts off. Could possibly be a valve or something not opening or closing properly??

Since new? How new is it?
Does this only do this in the heat pump mode?
Does it do this in the A/C mode?

Is it a two stage unit. Can you get the model number?

It could very well be a reversing valve noise. A fan motor can also make a similar noise if the capacitor is defective. Sounds and noises are extremely difficult to diagnosis when at the unit let alone trying to guess on the from a question on the board.

Your model also indicates you have a scroll compressor. While they are good compressors they can make noise during start up and shut down.

Try to listen a bit more intently to the unit and see if you can narrow it down.