If you are certain the mould is not the treatment as described under WHAT IS PRESSURE TREATED TIMBER? It is likely that the airflow is very low in your building which is not allowing trapped moisture to release.
Open doors and windows where possible.
Wipe the affected area with a diluted bleach solution
Ensure you open the doors as often as possible to keep the air circulating.
To avoid this happening, don't store items tight up to the walls, keeping a distance between boxes and other times to reduce trapped moisture. Do not store wet items in your garden building. Apply a water repellent to the exterior walls and/or line your building with a breathable membrane. You can also install vents to help airflow but this can be achieved by opening doors and/or windows regularly.