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Make sure you're in Object Mode. Press SHIFT-C to center the 3D cursor to location 0,0,0 ((x,y,z)
It's important that the cube and curve both share the same Origion point, so with the cube selected, press T to get the "Tools" panel up at left. Open the "Tools" tab at top left and select "Origin-->to 3D cursor"
Select the cube again, and in it's properites at right, click on the Constraint icon. (two links of a chain)
Also tick the "Follw Curve" box when you want the object to be facing forward and always aligned to the path as it travels.
With the mous cursor still in the Evaluation slot, press letter I again to create the destination keyframe.
If wanting to set a camera moving along the path, you might like to take a peek at the link mentioned above if the camera is a nervous passenger and gets the "jitters", literally!