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Do you want to change the bg of one block, or all blocks?
If it's all, take a look at mthe stylesheet (the .css file in the theme dir) and look up the class responsible for the block style. If it's just for one block, you could add a class/id to a td or div in the template of that particular block. add that class/id to your .css and input the style you want the block to have, in this case the background.