I don't get rotations between parent and child

Hello,

I'm trying to understand rotations between parent and child but I failed so far.
I have a parent game object. It's rotated 30degrees along the (global) x axis.
Then I set a cube as child and reset it. It is automatically tilted 30 degrees along the global x axis as well and in the inspector, for its rotation, 0 0 0 is marked.

Then I try to increase the field X for Rotation in the inspector for the cube. This move the local Z and Y axis of the cube, the X axis does not change. Surprise : if I then play with Z, it does not make rotate the cube according to the local Z axis from the parent but only according to the local Z axis from the cube which does not match with the local Z axis from the parent anymore since I changed X.

Once Z has been changed, changing again X makes rotate the cube around the X local axis from the parent (it seems like it).

Even more confusing: if I change then Y, it makes (apparently) rotate the cube around the local Y axis from the parent. But then, playing again with X makes rotate the cube around and axis... not matching with either the local X axis from the child itself or the parent. What's going on here? It seems completely random. What am I missing?