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First of all I will assume that by sugar we mean sucrose, which is the common table sugar.

Here is the structural formula for sucrose:

sucrose
_{Source: Wikipedia - Sucrose}

If you are not familiar with chemical structures for organic compounds, note that every "corner" in a chemical structure like this is considered to be a carbon atom (C), even if it is not written for visual clarity (there may also possibly be hydrogen atoms, see the Wikipedia page on skeletal formulae for an extended explanation)

Here is the formula for cocaine:

cocaine
_{Source: Wikipedia - Cocaine}

Here is heroin:

heroin
_{Source: Wikipedia - Heroin}

Obviously I could go on for a while listing all existing drugs but I guess there is no much point in doing that...

Now, if we take the claim literally, and we look at elements, then the claim is true. Sugar is made by 3 elements: carbon (C), oxygen (O) and hydrogen (H). Cocaine has the same plus nitrogen (N).

However, this is pretty meaningless as the majority of organic compounds contains C, O and H...

If the claim is to be read as one atom more then it is clearly false. And even if it were the case that would not imply absolutely anything in terms of the biological actions of either compound, as their 3D structures are clearly different.