Subject: Sugar/water solution

What I want to know is this:

--A gram of sugar also has volume.  Let's say it has 1 cc of volume.
--If you dissolve that gram/1 cc of sugar into 100 cc of water, do you
end up with 101 cc of liquid?
--If so, how do you explain that 100 cc of plain water has less mass
(weight)  than 100 cc of water with sugar dissolved in it?
--For example, a 12 ounce can of Diet Coke weighs less than a 12 ounce
can of regular Coke.
--I was thinking that there was a chemical reaction of sorts when
sugar dissolved with water which would not necessarily create a tit
for tat increase in volume.  As you know, there's lots of space
between those molecules to fill.
--I hope this makes my thoughts more clear.  

Re: Sugar/water solution