3 layers cake, cutted the top (levelled)
Did buttercream in between and on the sides
Fridge for 3hrs
Any future suggestions?
You might want to include your recipe for the buttercream. That could help people figure out one of the reasons for your cake layers sliding around.
My thoughts from looking at your luscious cake photo are:
3 layers is a pretty tall cake! 2 layers would be more likely to stay stable. If you want 3, you could make them thinner, or even cut one of them in half. As long as you don't have a sliced edge at the very top, it doesn't matter that frosting will kick up crumbs from the sliced edges.
Layers don't look quite level (i.e. flat). You mentioned leveling the top layer. Maybe more important to level the bottom layers, if you don't want the upper stories sliding around.
Is buttercream a little too liquid and slippery? Knowing your recipe might help people determine this.
Possibly a little tooo much buttercream in between layers. I don't mean too much to be delectable; I mean too much for mechanical stability. It's hard to tell how much is in between the layers, but it does look like a pretty thick coating on the outside, so I'm guessing you were also generous in-between.
All that said, this cake looks terrific, and very rich!
As tasty as that cake looks, I don't get the impression that the buttercream was very thick or was too warm. I would recommend looking for a thicker recipe.
I find that cake does not like large changes in temperature, and going from 30°C to 3-5 is not small by any stretch. If you've helped yourself to a cupcake that is still warm from the oven you may recall that it is lighter in consistency than when that same cupcake has been left to cool. The same thing is happening in the fridge but it also has the added weight of the other layers. Older fridges tend to be cooler towards the back as well, plus warm air comes in every time you open it. That might have contributed to one side being affected more than the other (if the cake was leaning towards the back of the fridge when it was pulled out that would support the theory).
I agree on the point about the amount of buttercream between layers. It's worth bearing in mind that on top of stability, the more buttercream between the layers the more you're expecting those eating the cake to consume, and for some that will get sickly. You just need a couple of millimetres worth between each layer to keep it secure.