You haven't said what the climate is like in your locality in terms of normal temperature range and humidity. In particular, how do the conditions you wish to create in the cellar compare to those found in the rest of your building and outside?
It may well be that the fan you have added is making matters worse. If you are blowing air out of the cellar, you must be drawing it in from somewhere else to keep the pressure balanced. Can you figure out where the air gets in? If that air is normally warmer and/or moister than how you are trying to keep your cellar, then that will add to the dehumidifier's work. The air might also be being drawn in past/through the earth surrounding the cellar, and picking up moisture on the way. I would certainly try switching off the fan for a while to see what effect that has on the amount of water produced by the dehumidifier.
I would also look for other potential sources of moisture. Do you have any other equipment in the cellar that could raise the humidity? Cooking, showering and drying clothes are typical culprits in domestic buildings - but a constant 40L/day is a lot of water, so it's more likely to be something that has gone wrong. Are there any signs of leaking water pipes? The air-con is worth investigating too. If it is operating in cooling mode, it will also produce condensation, like the dehumidifier. Is it draining properly? There's an outside chance it might even have a humidifier mode, and be fighting against the dehumidifier.
More likely though, I would guess that the moisture is probably coming from the soil around the cellar, through the walls and floor. What to do depends on how wet it is, and why. If it is not very wet, fixing the airflow might be enough to help. You might also be able to help matters by improving rainwater drainage around the building, or fixing a leaking pipe that is saturating the soil. If you can monitory the humidity or soil moisture, you may find you are gradually drying out the cellar's surroundings. But if you have a high water table in your area or lots of rain, you are probably going to need to try to make the cellar watertight. Without doing this, moisture is always going to diffuse from the damp surfaces into the relatively drier air produced by the air-con and dehumidifier.
Even if the dehumidifier is pulling in water from the surrounding soil, it may still be a viable solution if it is powerful enough to maintain the humidity you want. It depends whether you can identify and cut off the water source or not, and the balance of the cost and hassle of doing so versus keeping the dehumidifier running.
