I'm just confirming that the app Volume+ does successfully boost audio volume for the speaker phone (speaker on back of phone). It does Not require root to do this.

I have the paid version and I set it to amplify level 20. It doesn't seem to boost as much as I'd like, but that may be a limitation of the speaker.

You have to enable it under: Settings app > Sound > Music effects

Also, I do not know if it boosts the small normal ear speaker. I would have done more testing, but I'm lacking a microphone to accurately measure the audio volume. The difference while listening by ear is small to me. Let us know what your results are.