You can have VBA code that gets triggered when a cell is changed.
Formatting a cell to have a different color, though, does not trigger a change event, so just changing a cell fill will not fire up any macro.
Instead of formatting a cell with a fill color, you could enter a number or text into the cell. You can use conditional formatting that will change the color of a cell with a value.
Entering a text or number into a cell will trigger a change event, and that event can easily change the fill color of other cells.
So, set up conditional formatting if a cell contains a value, say, 1. If it's a 1, format it blue with a blue background fill. This way, the number won't be visible.
Then use this macro (right-click the Sheet tab, click "View Code" and paste the code into the code window)
Option Explicit
Private Sub Worksheet_Change(ByVal Target As Range)
If Not Intersect(Target, Range("D3:AH564")) Is Nothing Then
If Target = 1 Then
Target.Offset(0, 14).Interior.Color = RGB(146, 208, 80)
Target.Offset(0, 28).Interior.Color = RGB(0, 112, 192)
Target.Offset(0, 42).Interior.Color = RGB(146, 208, 80)
End If
End If
End Sub
It is not clear if the trigger cell can be all over the range or just in column D. The macro can be adjusted to accommodate whatever you define.
Edit:
If you copy and paste a value into multiple cells, then try this:
Option Explicit
Private Sub Worksheet_Change(ByVal Target As Range)
Dim cel As Range
If Not Intersect(Target, Range("D3:AH564")) Is Nothing Then
If Target.Rows.Count > 0 Then
For Each cel In Target
If cel = 1 Then
cel.Offset(0, 14).Interior.Color = RGB(146, 208, 80)
cel.Offset(0, 28).Interior.Color = RGB(0, 112, 192)
cel.Offset(0, 42).Interior.Color = RGB(146, 208, 80)
End If
Next cel
End If
End If
End Sub