See this post, it's older than that word:
Cushi is the Yahuuds n word
No, it doesn't. Cushitic comes from the North Sudanese Hamitic Empire of Kush (1,000 BCE). That's its direct etymology.
Cushi was only recently (post-1950s) degraded to ****** in modern Hebrew. It never meant that in ancient times. Lastly, the modern vulgar definition was mainly an insult towards Ethiopian Jews, who ironically are Cushitic. Later on as more African travelled to Israel it then got broadened to all SSAs. But who cares, nobody speaks Hebrew and it never meant that in ancient times.