I want to know if an aluminium lasagna pan can be used in an oven for baking a cake?
If you're asking if you can bake a cake in that aluminum tin because you're wondering if it's safe, then the answer is yes. It says Lasagna Pan on the label, as in you're meant to bake a lasagna in it. No reason why a cake would be dangerous. I imagine you'd be baking the cake at a lower temp than a lasagna.
You'd want to worry about the cake sticking to the sides maybe. You'd also want to account for the fact that the pan is thinner and heat transfer would be different (cooking times and temperatures might need to be adjusted).
Given that they sell pans that are identical in all respects except for being smaller for the specific purpose of baking cakes in them, I'm not sure what possible trouble you're anticipating.
Because of the large size of the lasagna pan, you might end up with a thinner layer of batter than you'd get in a cake pan; if so, reduce the baking time accordingly.
As mentioned by others, the thin aluminum will transfer heat faster than a thicker and/or non-aluminum pan would, so you may need to reduce the oven temperature a bit.
The non-smooth sides seem like they ought to cause sticking, but in actual practice, as long as you prepare the pans appropriately for your cake recipe (butter & flour vs. butter only), you shouldn't have any problem.
Yes, you can use an aluminum pan for lasagna, but you should add one or two Wilton cake "heating cores" or a Wilton cake "nails" in the middle. Google these items at Wilton. Prepare them by applying shortening and flour. Adjust oven temperature down 15-25° and add 15-30 min to your cook time. Begin monitoring it after the regular cook time approaches.