Do I have to wait until one month before the end of the contract period to cancel the contract?
No. To avoid a notice period after the binding period has ended, you can terminate the agreement in good time. If you have a notice period of one month, you can terminate the agreement at least one month before the binding period ends.
However, always check what is stated in your specific agreement regarding what applies, but if nothing is specified, you can theoretically terminate the agreement the day after you entered into the agreement to end when the binding period expires. Then the notice period is counted parallel to the binding period, and the agreement ceases immediately at the end of the binding period.
NOTE! However, be very clear about which date the termination should apply so that the service is not terminated immediately by mistake and you receive a final invoice.