Possible Color Combinations for RGB LED?

I was wondering what the number of possible combinations of colors/brightness is for 1 dotstar RGB addressable LED (APA102C driver). I made the following calculation but it seems very high and I wasn't sure exactly how many choices per Red/Green/Blue there were.

(256 brightness choices)(60 choices for RED)(60 choices for GREEN)*(60 choices for Blue)=55,296,000 possible color and brightness choices per led?

The controller seems to allow 256 steps of brightness for red, green & blue so that would be 256*256*256 = 16,777,216 colour combinations. You can ignore the brightness level adjustment as it just effects all 3 colours at the same time.

Basically a duplicate of what Riva said while I was writing this but a bit more information and I already had it typed out so here it is anyway:

I believe it's actually 8 bit PWM on each color but there are only 5 brightness bits(https://cpldcpu.wordpress.com/2014/08/27/apa102). So that gives: 32 x 256 x 256 x 256 = 536870912 possible settings. However, I don't think that is actually the number of possible colors because the different brightness values will just end up allowing multiple settings to result in the same color. Obviously brightness 0 will result in the same color(black) no matter what you have the RGB set to so that's 16 million duplicate settings right there. From the link I posted above, it sounds like the brightness feature has problems so it's better to just leave it at 31 and use the color values to set brightness. So really you have: 256 x 256 x 256 = 16777216 colors.

So why do you have such different values for the possible values of each setting? Probably it's something to do with the library you're using. Where did you get the information that there are only 60 values for each color?

I took a look at the Adafruit_DotStar library and they don't use the actual brightness feature of the APA102(https://github.com/adafruit/Adafruit_DotStar/blob/1.0.1/Adafruit_DotStar.cpp#L190-L198):

Although the LED driver has an additional per-pixel 5-bit brightness setting, it is NOT used or supported here because it's a brain-dead misfeature that's counter to the whole point of Dot Stars, which is to have a much faster PWM rate than NeoPixels. It gates the high-speed PWM output through a second, much slower PWM (about 400 Hz), rendering it useless for POV. This brings NOTHING to the table that can't be already handled better in one's sketch code. If you really can't live without this abomination, you can fork the library and add it for your own use, but any pull requests for this will NOT be merged, nuh uh!

So that verifies that if you're using that library the brightness settings is not actually using the extra 5 bits so the different brightness settings result in duplicate colors and thus that library definitely only allows 16 million colors.