Can I Implement Open Cycle Map on My Own Web Site?

I would like to create a cycling map for the area in which I live (south west Virginia), and I am wondering if I can somehow implement Open Cycle Map and take advantage to all of the cartographic enhancements that have been made to that map. Is it possible to use Open Layers and pull in Open Cycle Map while also customizing the display (i.e. adding other layers to display)?

I figured it out. Do I need to get in touch with the creator of open cycle map and let them know/ask permission?

No that’s what they are supposed to be used for.

The normal OSM attribution still stands though.