How to attach camera to player in a right way

Hi I'm new to unity so I decided to make simple things, I create a cube and give it movement up/down for advance, and left/right for rotation works fine, but I attach the camera to the player for the following of the "character" and when the camera is attached to the player the coordinate system automatically moves from the cube to the camera and now I'm moving the camera not the cube, and the change of directions seems weird because before the player rotates over their own body now rotates around the camera, and the camera is a child of the character

there is a way to attach the camera and remain the coordinate system in the player/character?

Before Attachment After Attachment