any number of times; as many times as it takes; over and over
Emphasizes repetition without limit; often used to express persistence or willingness to repeat an action indefinitely.
失敗しても、何度でも挑戦する。
Even if I fail, I'll try again as many times as it takes.
この曲は何度でも聴きたくなる。
I want to listen to this song over and over again.
If you don't understand, feel free to ask as many times as you need.
It's okay even if you fail—you can always try again as many times as you need.
幾度も is a more literary way of saying 'many times', while 何度でも stresses that the action can be repeated without any limit.
何度も describes an action that actually happened many times, whereas 何度でも means 'as many times as one likes', used for offers or permission.
Compound of 何度 (how many times) + でも (even if, no matter). The combination yields the meaning 'no matter how many times'.