You could achieve this using Conditional Formatting and SUMIF formula to achieve this

I've used the following conditional formatting rules (You will need to change this for your ranges)

The conditional formatting is applied to both the cell fill and also the font text colour (to make the True/False be 'invisible')

In cell C6 (a merged range) I have the formula

=SUMIF(3:5,TRUE,3:5)

Where cells in the D range contain the values of the linked cells for the checkboxes (i.e. True, False)and C range is the values you want to sum.

This is a much simpler approach then any VBA solution and personally, I'd remove the formatting of the cells from your vba above and just use the conditional formatting.

If you're looking for a VBA way to initiate this (except for the SUMIF formula) I've updated your below code to add the conditional formatting

Sub Insert_Checkbox_Link_Cell()
    Dim rngCel, myCells As Range
    Dim ChkBx As CheckBox
    Dim cBx As Long

    Set myCells = Selection
    myCells.NumberFormat = ";;;"

    Application.ScreenUpdating = False
    For Each rngCel In myCells
        With rngCel.MergeArea.Cells
            If .Resize(1, 1).Address = rngCel.Address Then
                Set ChkBx = ActiveSheet.CheckBoxes.Add(.Left, .Top, .Width, .Height)
                With ChkBx
                    .Value = xlOff
                    .LinkedCell = rngCel.MergeArea.Cells.Address
                    .Text = ""
                    .Width = 18
                    .Top = rngCel.Top + rngCel.Height / 2 - ChkBx.Height / 2
                    .Left = rngCel.Left + rngCel.Width / 2 - ChkBx.Width / 2
                End With
            End If
        End With
    Next rngCel

    With myCells
        ' Set default value
        .Value2 = False
        ' Add conditional formatting for False value
        With .FormatConditions
            .Add Type:=xlExpression, Formula1:="=" & myCells.Cells(1).Address(False, True) & "=False"
        End With
        With .FormatConditions(.FormatConditions.Count)
            .SetFirstPriority
            With .Interior
                .Pattern = xlSolid
                .PatternColorIndex = xlAutomatic
                .Color = 9868950
                .TintAndShade = 0
                .PatternTintAndShade = 0
            End With
            With .Font
                .Color = -6908266
                .TintAndShade = 0
            End With
        End With
        ' Add conditional formatting for True value
        With .FormatConditions
            .Add Type:=xlExpression, Formula1:="=" & myCells.Cells(1).Address(False, True) & "=True"
        End With
        With .FormatConditions(.FormatConditions.Count)
            .SetFirstPriority
            With .Interior
                .Pattern = xlSolid
                .PatternColorIndex = xlAutomatic
                .Color = 52377
                .TintAndShade = 0
                .PatternTintAndShade = 0
            End With
            With .Font
                .Color = -16724839
                .TintAndShade = 0
            End With
        End With
    End With

    Application.ScreenUpdating = True
End Sub

When a checkbox is checked, the value of the cell is TRUE, not CHECKED.

2.

The rownumbers of the ranges in 1 formula must be the same;

you used B8:B14 and H8:H13,

it must be: B8:B13 and H8:H13

or B8:B14 and H8:H14

3. The solution of 'Snow Lu MSFT' is correct, but you also can use: =SUMIFS(B8:B14,H8:H14,TRUE)

The checkbox can be linked to a cell which would contain the value of TRUE or FALSE:

=IF(B1,0,SUM(A2:A200))