There are multiple ways with and WITHOUT cable to watch ESPN on your XBOX.
First there are multiple apps in the app store for ESPN including ESPN 3 and ESPN+, but live broadcasts aren’t typically in these on demand apps.
To have live broadcasts the simplest thing is to do is to sign up for Sling TV, Hulu w/Live TV, or Youtube TV. The package with ESPN in it will run you about $50/mo if you want a decent sized bundle surrounding ESPN.
If you are looking for JUST ESPN, the cheapest package is from Sling. This cost is $25/mo and includes all the Disney owned channels including multiple ESPN channels, plus other channels including Comedy Central.
If you are still using cable, you can connect any cable box to you XBOX via an HDMI in cord option, then open the “app” for that device plug in port. It can actually plug in Rokus, even Playstations but is optimized for cable equipment.