A week without resupply,lightest food.

Protein 1 gram = 4 calories
Carbohydrate 1 gram = 4 calories
Fat ! gram = 9 calories

From the above, you can see that fat contains over twice the calories per gram than either protein or carbohydrate. So foods with more fat are more calorie dense. Nuts are good for packing energy because they have some good omega-3 fat in them.

I don't think eating only ganola bars for several days will make you sick from malnutrician, but you may get sick of, i.e. tired of, eating them.

Rumi

Agree with Rumi. When I traveled Europe on a few bucks a day, I ate a lot of bread and cheese, with apples and carrots on the side. Those aren't quite as cheap here as they were there, but it's not bad from a $$ perspective, though heavy. On the other hand, if you do this, especially on a bike, you shouldn't need to carry more than a day or two of food at a time, so I'd go for more weight but also more taste and nutrition. Most granola bars are mostly sugar, so while you might not get sick, it's not all that great an approach for maintaining the energy levels needed for a trip like that.

Good question, though given the budget suggested by the OP's other questions, I'm guessing no. If you are taking a stove, there are lots of cheap, light options at the grocery store (think Lipton sides, etc.). They are high in salt, low in nutrients, but they'll get you through (I know. I did a lot of backpacking on those things when I was a starving grad student).