High power LED strip power distribution
I want to power 20 RGBW LEDs. Each of these lamps and each color channel should be individually controllable with PWM. Since it concerns pure LEDs without internal control I would like to use a PCA9632 for each lampe for each channel. Now each color channel needs about 3.2V at 0.7A. The IC doesn't manage this power of course. Therefore I want to install 4 constant current drivers each.


This is basically the right idea if you want individual "pixel" control of the LEDs.  If the distance between the LEDs and controller isn't huge (like they're actually pixels in a grid or somesuch), you should be able to use the I2C controllers to drive current controllers for each channel. 


  If I would now take a constant voltage source and connect the lamps parallel to it, a total current of up to 56A could occur which in many respects is very impractical and hardly feasible.


Yeah that could be a fair bit of extra copper. If you are using the right type of constant current driver for the LED it shouldn't expose the LED to a nasty voltage, but it wouldn't be a horrible idea to check as LED efficiency is sensitive to instantaneous voltage.


  Therefore I would like to use a voltage source with approx. 24V or higher to transfer the power with thinner cables and somehow reduce the 24V to 3.2V or so far that exactly 0.7A flows through the LED.


You'll need 1.5khz PWM suitable current controllers between the voltage source and the LEDs anyway, and the purpose of these is to perform this voltage reduction. 

If you want, you can hard switch them to the PWM signal from the I2C controller, in which case you should have localized voltage drivers for each LED color to split up your potential 56A, which isn't a horrible way to go(but requires greater confidence in your cooling solution if there is no current control, so current control is highly recommended) or inline resistors(yuk).  This is easier to execute if the "pixel"s are physically close so you can group a bunch of greens, bunch of reds, bunch of blues, etc.

Rather than running all of the channels at 700mA max, you should tune the RGB channels by running each or all 3 of RGB at 700mA and seeing which one is dimmest, then tune the other two down to that brightness as they likely won't be perfectly matched at 700mA.  This way in your software, 100% will really be 100% and you won't have to worry about software tuning the brightness as much.  You only have 256 brightness levels, so if you do too much tuning in software your color resolution will suffer.

There are other ways to control LEDs too, but regardless of the method you choose, you will need to design your cooling solution to be able to shed ~200W at full brightness without letting the LEDs become too hot.  Erm...  Unless you're really certain you need 150W of RGB light, you might want to consider ordering a few high power RGB LEDs and doing a mockup of a single pixel to confirm that brightness level(and therefore thermal design) is really necessary.  This would also give you a chance to get the I2C driver, the current controller and the LED as close together as possible and use an EMI tester if you want.