How to change each uitableviewcell background color

You need to delete this line

let cell = tableView.dequeueReusableCellWithIdentifier("cell", forIndexPath: indexPath) as! GroupTableViewCell

from your willDisplayCell function, because it already have your cell in parameters, and you just overriding it with new cell, and your new cell will be never used.

If you want to show colors in order, then you can use indexPath:

var cellColors = ["F28044","F0A761","FEC362","F0BB4C","E3CB92","FEA375"]
func tableView(tableView: UITableView, willDisplayCell cell: UITableViewCell, forRowAtIndexPath indexPath: NSIndexPath) {
    cell.contentView.backgroundColor = UIColor(hexString: cellColors[indexPath.row % cellColors.count])
}

Make an array with the colors, maybe you have to create them dynammically but in this example they are hardcoded.

let bgColors = [UIColor.blackColor(), UIColor.grayColor(), UIColor.whiteColor()];

Then in your cellForRowAtIndexPath take the color at the correct index and set it for the cell. I don't know your actual setup but something similar to this should work.

let bgColor = bgColors[indexPath.row]
cell.contentView.backgroundColor = bgColor