Yes, you can: How to play Xbox 360 games on Xbox One – GeekWire
Official Xbox 360 HDMI Cable (Xbox 360) : Video Games - Amazon.com
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
How to: Connect Xbox 360 AV & HDMI at the same time - YouTube
Amazon.com: Xbox 360 HDMI Cable : Video Games
Amazon.com: Microsoft Xbox 360 Black HDMI Cable (Retail Packaging) : Video Games