Change color of all cells on sheet based off of one cell value

I've tried a handful of things to accomplish this and have hit a number of dead ends - I'm sure one one of you has seen this before though.

I want to change the fill color of all cells on my sheet, based on the value of one specific cell. In my sheet, I am using cell F1 as the trigger for the change.

If the word Blue is in the cell, I want the background color of all cells to be Blue. Likewise for Red and Yellow as well.

I don't believe conditional formatting can get this done, as all but the one cell (for this) will be empty. Please let me know what ideas you have for getting this done.

Thanks in advance.