How to calculate the deflection of beam that is reinforced through formula?

You assume a new section by multiplying the area of the steel by the ratio of modules of elasticity of steel over aluminum while keeping the counter of messes at the same point.

You can just multiply the X dimension of the steel by n= Es/Ea, if the beam is loaded on Y direction. The tube will turn to an oval cylinder. Or you can just add a square section with area a = Atube * n - Atube at the center of the tube.

Then you calculate the second area moment, I , of this new section treating it as all aluminum and apply deflection equations as you'd to a simple beam.

I guess the given beam dimension is "H" x "W" X "t". If so, the two beams are loosely fit, and will act independently until one touches the other. Before then, there is no load sharing; after then, the steel beam will take the majority of load.