I have a few xbox classic games but my xbox is broken... so can I play them on a 360 / xbox one

or I should thrown them all in garbages?

Xbox does this lovely thing called backwards compatibility. Some of those old games may work on newer consoles, and even benefit from the power increase on an xbox one.

For a full list of backwards compatible titles, go here: https://www.xbox.com/en-US/xbox-one/backward-compatibility

Def don’t throw them in the garbage ffs.