You can replace the explicit Times operator with one that doubles:
expr = 4 x^2 (4 Subscript[a, 1] + Subscript[a, 2] - 7 Subscript[c, 4]); expr /. Times :> (2 ## &) 8 x^2 (8 Subscript[a, 1] + Subscript[a, 2] - 14 Subscript[c, 4])
## is shorthand for SlotSequenceSlotSequence[], and 2 ## is Times[2, ##]