Google-sheets – Partial Font color in a cell

Use the following code to accomplish your goal.

Code

function onOpen() {
  SpreadsheetApp.getUi().createMenu('Custom Format')
    .addItem('Max & Color', 'getmaxColor').addToUi();
}

function getmaxColor() {
  var ss = SpreadsheetApp.getActive(), aRange = ss.getActiveRange(); 
  var data = aRange.getValues(), colors = aRange.getBackgrounds();
  var dest = aRange.offset(0, data[0].length, 1, 1);
  var index = getmaxIndices(data);
  var max = data[index.i][index.j], color = colors[index.i][index.j];
  dest.setValue(max).setBackground(color);  
}

function onEdit() {
  var ss = SpreadsheetApp.getActive(), col = ss.getActiveCell().getColumn();
  if(col < 7) {
    var aRange = ss.getRange("A1:F7"), data = aRange.getValues();
    var colors = aRange.getBackgrounds();
    var dest = aRange.offset(0, data[0].length, 1, 1)
    var index = getmaxIndices(data);
    var max = data[index.i][index.j], color = colors[index.i][index.j];
    dest.setValue(max).setBackground(color); 
  }
}

function getmaxIndices(data) {
  var max = 0, indexI = 0, indexJ = 0;
  for(var i=0, iLen=data.length; i<iLen; i++) {
    for(var j=0, jLen=data[0].length; j<jLen; j++) {
      if(data[i][j] > max) {
        max = data[i][j], indexI = i, indexJ = j;
      }
    }
  }
  return {"i":indexI, "j":indexJ};
}

Explained

The onOpen() adds a menu item. Select the range you want to evaluate and select the menu option Max & Color. The values and backgrounds are collected as is an offset range. Then the indices (2d-array) of the max value are obtained, through the getmaxIndices(). Afterwards the corresponding max value and color is set.

The onEdit() does almost the same, but it has a fixed range. It will only fire if a cell is edited and if the edited cell belongs to the A1:F7 range.

Note

The reason for getting the error message, can be read in this answer: custom function

Example

I've added the sample code into your example file.

The only way I know is to use a 'dummy' parameter to the function, that is not really used in the custom function, but will trigger the function to recalculate. So, where you would normally use:

=sumWhereBackgroundColorIs(color, rangeSpecification)

you would now use

sumWhereBackgroundColorIs(color, rangeSpecification, F1)

In F1 (or any other cell you may want to use) you can have value (e.g. 1) that when changed (e.g: incremented with 1) will force the recalculation of the custom function. This 'incrementing act' can also be scripted.