Is there any way in which you can download Shivering Isles for the 360 of course for free

As far as I know, there is no legal method for getting The Elder Scrolls IV: Shivering Isles on the XBox 360 without paying. I do believe that they offer a trial version that you can download from XBox Live, though you will have to pay approx. $20 to $30 to get the full game.