Duplicated objects, different colors

hey, I was wondering if anyone could tell me how to break the link between two duplicated objects, so that I may give them different colors, etc.

To give some more details, I mean if you have made a cube, then in the hierarchy window, you right clicked that cube and selected duplicate, what happens then is that if you change the color of any of them, both changes color.. So I was wondering if there is a way to "break the connection" between the two dupes, so that they may be changed separately?`

Thank you again for being awesome and answering my noob questions! :)