Macro code to copy a cell and paste it to the next 2 cells

Try

Sub copycell()
    For i = 1 To 1000 Step 4
        Cells(1, i).Copy
        Range(Cells(1, i + 1), Cells(1, i + 3)).PasteSpecial
    Next i
End Sub

or simply

Sub copycell()
    For i = 1 To 100 Step 4
        Range(Cells(1, i + 1), Cells(1, i + 3)).Value = Cells(1, i).Value
    Next i
End Sub

Step keyword is used to specify a different increment for the counter variable of a loop. Step changes the value used to increment the counter. In this case, i will increment by 4 i.e. from 1 to 5 then to 9 then to 13 and so on...

Above code will copy cells in a row across to the right.
If you want to copy cells down in a column then you can use following code.

Sub copycell()
    For i = 1 To 100 Step 4
        Range(Cells(i + 1, 1), Cells(i + 3, 1)) = Cells(i, 1)
    Next i
End Sub

Here it is, 4 steps between each loop in order to move to the fifth cell from the first cell.

Sub copycell()
for i= 1 to 1000 step 4
Cells(1,i+1) = Cells(1, i)
Cells(1,i+2) = Cells(1, i) 
Cells(1,i+3) = Cells(1, i)      
next i
End sub