I think the short answer is that there is no direct conversion between cp and watts without specifying the construction and operating parameters of the bulb.
The wattage of a blub refers to the power consumed and – for simple resistive circuits (i.e., no inductive or capacitive components) – can be calculated by any of the means posted above (i.e., current in amps squared times resistance in ohms or voltage in volts times resistance in ohms, etc.).
The candlepower of a blub refers to the luminous intensity emitted by the bulb and without getting into filament construction, blub envelope material, etc., the luminous intensity depends on the wavelength of the emitted light, the standard against which it is measured, the use of built-in reflectors (reflective coating integral to the light bulb envelope) and other parameters. In trying to avoid some “Beam me up, Scotty” responses to this reply, the simple example is that the candlepower of a bulb that draws (for example) 2 watts could be the same as the candlepower of a bulb that draws 3 watts, or - to state the converse - two differently constructed bulbs that each draw 3 watts, could have different radiant power, that is, different candlepower.
Now, for the “Beam me up, Scotty” (technically “Scotty, beam us up”) answer: As you will recall from kindergarten, candlepower measures luminous intensity (in candelas, sometimes referred to as ‘candles’). Specifically, one candela is one lumen per steradian (1 cp = 1 lumen/steradian). (I don’t think they covered ‘lumens’ until first grade, and I’m certain they didn’t cover solid geometry and such items as steradians until second grade, but in the event, a lumen is a unit of luminous flux, which is radiant power tempered by the response of the human eye.) As we all know, the average Mark 1 Mod 0 human eye has a peak response to bright light at a wavelength of about 555 nanometers, roughly the wavelength of green light (deep red is about 700 nm and violet is about 400 nm). At this frequency (wavelength being related to frequency by the speed of light) one watt of radiant power equal 683 lumens, whereas one watt of light at other frequencies – colors; i.e., of greater or lesser wavelength - will equal fewer lumens inasmuch as the light is being emitted at a wavelength that the human eye is less sensitive to.
A steradian is a unit of solid angle and as everyone knows, there are 4pi steradians in a sphere. For an isotropic light source (one that radiates equally in all directions, a physical impossibility if you consider the construction of the typical light bulb) a 1 candlepower blub would produce 1 cp x 4pi steradians = 1 lumen/steradian x 4pi steradians = 4pi lumens (about 12.6 +/- lumens) of radiant power. Using the ‘1 watt of radiant power at 555 nanometers = 683 lumens’ from above, our 1 cp bulb producing 4pi lumens = 12.6 lumens/683 lumens-per-watt = 0.0184 watts of radiant power.
In the case of a bulb producing “white” light (that is, light composed of all, more or less, frequencies - or wavelengths – of light) a 1 cp bulb would “equal” only about 0.014 watts, depending on the actual “whiteness” (sometimes referred to as the ‘temperature’ frequently in degrees Kelvin) since – as stated above - the response of the average human eye is less for light produced at wavelengths other than 555 nanometers.
Scotty? Hello? Scotty, are you there…?
And, "yes" it IS a slow day out here on the west coast.
