There are two types of nest box to choose from – internal to the cage and external to the cage. Today, it is generally recommended to use externally mounted nest boxes. These of course use up valuable room in a small birdroom so for a small shed I would suggest that they are placed inside the breeding cage.
While not utilising any space this can present further problems, the first being access to the chicks for checking, cleaning and ringing purposes and so therefore the nest box door should be accessible. To give the hen privacy when incubating the eggs, the entry hole should be facing the back of the cage. The other problem is that budgerigars are very destructive, and the box will be badly chewed and needs to be of strong construction.