Source XLR to Balanced Preamp will increase gain?

In many cases, but not always, there will be a 6 db increase going from unbalanced to balanced, everything else being equal. It depends on the designs of both of the interconnected components.

But also, of course, as Jcharvet pointed out different CDPs may have different output levels for the same connector type. So everything else may not be equal.

From an article on the web, I got this formula:

3dB = doubling the amplitude. If you have a reference signal at 1 volt, 3dB is 2volts, 6dB is 4 volts, and 9dB is 8 volts.

That is not correct. A 3 db increase = doubling of power. A 6 db increase = doubling of amplitude/voltage, which corresponds to a 4x increase in power. (As you may recall, power is proportional to voltage squared, for a given impedance).

To be completely precise, this assumes that impedances remain the same as power or voltage is doubled.

Regards,
-- Al

If I choose a CDP with say, 4V output at XLR, will it mean that my amp will ultimately see 8V at the MAX level of the preamp's output?

Assuming you are referring to an active (not passive) preamp, when its volume control is at max its output voltage will usually be several times or more greater than its input voltage, regardless of whether balanced or unbalanced connections are used. In other words, an active preamp applies significant gain to the signal internally, for both types of connections, when its volume control is at max.

Regards,
-- Al

Thanks, Milpai. Adding to Ralph's response just above, I'm not certain that it would be safe to assume that a TVC will necessarily be designed to provide unity gain at its max volume setting, for either kind of input (RCA or XLR). I wouldn't be surprised if at least a few of them are designed to provide a few db or more of voltage stepup at their max volume setting. (As you most likely realize, a transformer can be designed to boost voltage, although it can't boost power).

And to add further uncertainty, I'm not sure that different manufacturers are always consistent with respect to whether amplitudes and gains for balanced interfaces are specified with respect to the voltage on each leg, or to the voltage difference between the two legs (which of course would be twice as much).

Regards,
-- Al