Can I map a hostname and a port with /etc/hosts?

No, that's not possible. The port is not part of the hostname, so it has no meaning in the hosts-file.

If you really need to do this, use a reverse proxy. For example, with Nginx:

server {
  listen       api.mydomain.com:80;
  server_name  api.mydomain.com;
  location / {
    proxy_pass http://127.0.0.1:8000;
  }
}

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