Firstly, open the Castbox app on your iPhone or iPad and choose the episode you want to get started with.
Click the player bar at the bottom to enter the now playing page, tap the cast button at the top right hand side and then choose your HomePod speaker.
Alternatively, if you're already listening to Castbox on your iPhone and you want to switch the sound to your smart speaker, you can do so without opening up the app. From Control Center, the music tile will show the episode you're currently streaming on your phone.
Simply tap the icon at the top right side of the music tile or 3D Touch (or long press if you've got an older iPhone) and press the AirPlay button. Select your HomePod speaker and the podcast will stop playing on your phone's speaker (or headphones) and transfer immediately over to your HomePod. You can also use the widget on the iPhone's lock screen to do the same thing.
You can also use Siri Shortcuts to instantly play Castbox on HomePod.