Synthetic backup after a Cumulative incremental backup?

If your cumulative incremental backup means backing new and changed files since the last full backup, then you should use the term differential backup when talking about BE. Likewise, if differential incremental backup means backing up new and changed files since the last incremental or full backup, then use the term incremental backup.

Assuming that my interpretation of your terms are correct, you cannot do a differential backup and then a synthetic backup.  This is by design.  A synthetic backup is meant to aggregate one or more incremental backups with the last full backup into a new full backup.

When you create a schedule backup job which includes a synthetic backup, you will get a full backup job, an incremental backup job and a synthetic backup job.  It is up to you to edit each of these jobs and change the schedule to your liking.  For example, you can schedule the full backup job to run monthly, the incremental backup job to run daily and then the synthetic backup job to run weekly.

I would suggest that you read the Admin Guide on how to schedule jobs.