What do you have for breafast every day? ("Every day" here is two words. "Everyday" is a word but it's an adjective. Investigate further with your dictionary.)
1. I usually have a cake, corn, chicken soup & orange juice for breakfast.
2. I usually have a cake, corn, some chicken soup & some orange juice for breakfast.
Which of the above is correct?
"A cake" sounds a little odd, at least in BrE where it would be very unusual to eat a cake or any cake for breakfast. The same goes for corn but again, I don't know what you actually eat for breakfast. However, on the assumption of course that you personally do eat cake for breakfast, I would go with:
I usually have cake, corn, chicken soup and orange juice for breakfast.
The fact that you only have some/a certain quantity of each item is implied.
For me: I usually have toast and tea for breakfast.
I sometimes have cornflakes and orange juice for breakfast.
I occasionally have vegetarian sausages, vegetarian bacon, baked beans, hash browns, fried eggs, fried tomatoes, fried mushrooms, eggy bread and tea for breakfast!
Unless you only have one single item of a particular food, then there is no need for the indefinite article. If I wanted to be very specific I might use articles/numbers:
I occasionally have two vegetarian sausages, three rashers of veggie bacon, baked beans, two hash browns, a fried egg, some fried tomatoes and fried mushrooms, two slices of toast and a huge mug of tea for breakfast.
I don't like the use of the ampersand (&) in written English either. Use the word "and" on the forum. Also, have a quick check on the positioning of your commas. Remember that we do not put a space before a comma, but we do put a space after one.