When you’re installing a non-metallic electrical cable, you must identify the sections of the cable: the outside sheath (the jacket) and the interior conductors. What seems to be colored “wire” is really a sheath that covers the copper wires within.
To create holes, use a brace and bit to drill through the flooring, and then a keyhole saw to widen the entrance. Make sure that the holes are not exactly above a floor joist when you drill them. In fact, the joists & studying must be spared as much as possible while installing the water heater equipment.