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
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.