To sync your Productive account with Google and/or Microsoft Office 365 calendar, go to Settings - Personal Integrations:
Navigate to the calendar you want to connect and click on Connect calendar:
Log in to your account and the connection will show as enabled:
💡 The Google calendar integration is not possible to create via iPhone or iPad app. Instead, try creating it using the desktop or web app after which you will be able to normally use it on mobile devices.