I want to bake a cake but I don't have light brown sugar. Can I replace it with white sugar?
The result might not be exactly the same (in color/taste/texture), but basically, the substitution will work. Textural change will be due to the original recipe taking advantage of the molasses content of what is commonly sold as brown sugar.
You can substitute white sugar for light brown sugar with no problem, in my experience.
Make sure you substitute by weight (grams/oz), and not by volume(cups/spoons). This is because brown sugar is slightly more dense, so you get more sugar in a cup than you do with light brown.
You can make brown sugar from white sugar if you don't have brown sugar on hand. As explained on Cook's Country (paywall):
In the test kitchen, we’ve found that pulsing 1 cup of granulated sugar in the food processor with 1 tablespoon of molasses makes a fine substitute for light brown sugar. For dark brown sugar, use 2 tablespoons of molasses for the same 1 cup of granulated sugar.
THE BOTTOM LINE: Don’t have any brown sugar in the cupboard? Make your own by mixing molasses into white granulated sugar. Or simply add the molasses along with the wet ingredients in your recipe.
Yes, you can substitute brown sugar with white sugar but brown sugar is usually less sweet so I would suggest ever so slightly increasing the amount sugar you put into the cake mixture.