Driving a speaker directly through an audio DAC?
If you're going to be using just the STM to drive a speaker, the main limiting factor is the current handling capability of the pins of the microcontroller. 


You didn't mention what power you want coming out of the speaker, but let's take a look at what the microcontroller can provide. Its working voltage range is 1.7 V to 3.6 V. According to absolute maximum ratings, the maximum current for any pin is 25 mA. So rough calculation is 3.6 V times 25 mA is 90 mW. This is the point where you can expect that your pin is going to burn out. Do note that to be able to reach this rating, you'd need a special high-impedance loudspeaker. This pretty much means that for any usable power level with a loudspeaker, you'd need an external amplifier. It might be OK for headphones though.
How does the math work? Well to put it simply, you have a speaker with its nominal impedance. You also have the voltage and current ratings for the amplifier or DAC. You would also need to take a look at the efficiency graphs in the datasheet to see how well would the amplifier work. In general, you're expected to use DAC only to provide a signal and then use an amplifier to drive the transducer. There are some DACs with integrated amplifiers though. 
In general, DAC is a component inside of a codec. Usually, a codec will have for example needed circuitry for a microphone input, have controllable gain, have some filtering inside of it and so on. A DAC will just to the digital to analog conversion.


As noted in the comments, you'd need to check if your microcontroller actually has a DAC inside of it. I can't see it on the datasheet. Are you maybe using a development board with this micro on it? In that case, the board might have its own DAC connected to the micro.