Whichever Xbox you're giving to your nephew would need to be the one that is your account's Home Xbox, in order for him to have access to the content on your account (including Live Gold). Your nephew can create his own account and use it to play anything that's been installed and is associated with your account on that Home console. If he were to login with his account on a console that isn't your account's Home console, he would only have access to any content/subscriptions that are associated with his account alone.
To my understanding, if the Xbox that is set as your "Home" console has active Live Gold, any Xbox Live account that signs in on it will have shared access to all the content. For example, before I bought my own Xbox One, I logged into my roommate's with my Live account and I was able to play any of the games he had installed. That's why quikah recommended you give your nephew the Home console linked with your account - so he could have access to all of the content that's associated with your account, which you'll have access to by virtue of logging in with your account, no matter what console you're logging in on.
If you already have an Xbox Live account, the easiest way is to login with your account on whichever Xbox you're wanting to give to your nephew, and designate it as your Home console. The link that quikah shared has instructions on how to do so mid-way through the page, under "Designate an Xbox One console as your home Xbox." After you've done that, he can login with his account and access any content/subscription stuff associated with your account on that Home Xbox.
I'm not 100% on whether you'd be able to play the same game on two different consoles at the same time. If imagine that it wouldn't work and would either boot the non-account owner once the account owner launches the game or it would give a message/error that the content is currently in use, or something like that. You can definitely both play at the same time on the same console... Just uncertain of how things shake out with multiple consoles at the same time. Perhaps quikah has some insight on this.
I know all this can be a little confusing when you're first delving into it - I know it was for me. Good luck everything configured to your liking!