The fructose part of sugar is metabolised straight to fat in the liver - so those people who call full sugar coke "full fat" aren't actually too far off the mark, however (un)intentionally.
Think about ecological/evolutionary processes... we get fruits available in late summer to autumn when animals (& humans without access to 24/7/365 supermarkets) at just the time when they need to massively fatten up to survive the lean winter & hibernation months. Fructose is a super-nutrient in that respect, it punches well above its molecular sibling glucose in promoting fat storage. Problem comes when "advanced" humans invent supermarkets, fast food drive thru's and the mile long treat food aisle in Home Bargains 
OP, read David Gillespie's book Sweet Poison, watch "That Sugar Film" about the hidden sugars in everyday savoury/breakfast food. Switch the coke for the diet version temporarily, I'm militantly anti artificial crap, but it's preferable to consuming large doses of fructose, the dangers of which are only beginning to be recognised and accepted. I have the occasional dcoke myself (once/twice a year)... totally given up fruit juice/soft drinks otherwise now. I have a small piece of solid fresh fruit after a meal now if I want something refreshing, eg berries lightly smushed into greek yoghurt or 1/4 orange.
The problem with the internal combustion engine/ thermodynamics metaphor for CICO is that humans & other advanced organisms are highly complex biochemical and endocrine powerhouses. Subtle changes in hormone levels can produce big changes in the body, insulin, in response to sugar intake is one of the main ones, and has significant anabolic properties... makes you bigger. It's why there's a specific type of anorexia among some T1 diabetics, who try to inject the minimum amount of insulin possible, in order to become skinny.
The ideal for the rest of us who desire to maintain a healthy weight is to eat a low insulinogenic diet, food that produces a low blood sugar response. All sweet fructose containing food, including table sugar, honey, syrups, soft drinks, sauces, sweetened processed food like cakes bread & biscuits give the swerve; also go easy on starchy carbs... a small serving spoonful of brown rice or a couple of new potatoes is fine, but not oodles of spaghetti or risotto or champ etc. The ideal is a regular size steak or chop or chicken potion, the fill the rest of the plate up with raw fresh salad with evoo & vinegar, or buttery lightly steamed mixed veg.