How can I remove the ends of this tap spout?
Wow, I haven't seen separate hot &amp; cold taps in a long time. I'd say it's time for an upgrade. It looks like you've been after that pictured one pretty good. I'd spray them inside &amp; out with vinegar a half dozen times throughout an entire day &amp; then run the hot water one for a minute.

The hot water would heat it up &amp; hopefully loosen everything, including any mineral deposits that the vinegar broke-up. Then, give it another jerking twist, rather than a slow torqueing twist. If that all works on the hot side, then you'd pour hot water over the vinegar-ed cold tap until that's heated.

I can't make out if the black plastic piece is hollow or not. But, if it is I think your only other option is to use an Internal Pipe wrenching bit of the right diameter, like this.