Yes, you can: How to play Xbox 360 games on Xbox One – GeekWire
Amazon.com: Y.D.F Xbox 360 HDMI Converter, Xbox 360 to HDMI Converter HD Link Cable for Xbox 360, Xbox 360 to HDMI Support 720P / 1080P. Compatible with Xbox 360 and Xbox 360 Slim. : Video Games
Broken HDMI port on Xbox 360 slim, how can I fix this? : r/xbox360
How to Hook Up XBox 360 to a TV – FireFold
File:Xbox 360 HDMI Cable.png - Wikipedia
Xbox 360 HDMI Conversion Kit review: Xbox 360 HDMI Conversion Kit - CNET