As commented, just in case the link I posted there broke, try this:
Add a Name(any valid name) in Excel's Name Manager under Formula tab in the Ribbon.
Then assign a formula using GET.CELL function.
=GET.CELL(63,INDIRECT("rc",FALSE))
63 stands for backcolor.
Let's say we name it Background so in any cell with color type:
=Background
Result:
Notice that Cells A2, A3 and A4 returns 3, 4, and 5 respectively which equates to the cells background color index. HTH.
BTW, here's a link on Excel's Color Index