How does sugar influence the taste? I have been told that sugar adds a sour taste to the coffee.

Personally I do not put sugar at all in my coffee but I was wondering for the sake of curiosity... Also I always preach to people that do put sugar in about how it ruins their coffee, due to the sour after-taste the sugar is adding.

Is there any chemical reaction here between the sugar and the coffee? Is it a result of a mixture between bitter and sweet that creates the sour taste?

When I tried having coffee without sugar I did feel like there is this sour feeling to it, but I also sometimes taste it with espresso made from some blends.
Sugar adds a sweet taste to coffee, not a sour taste.  Sourness and sweetness are rather separate tastes! Different flavours will to some extent interact with each other, and individual preference and taste have something to do with this, but there are particular causes of certain flavours.

Sourness is a perception of acidity. In high enough quantities, sugar can overwhelm the perception of acidity (e.g., cola has a pH ~2.5, but doesn't taste sour because the perception is overwhelmed by sugar/sweetness; see also this Seasoned Advice question on sugar reducing perception of sourness). I don't see how sugar could be the cause of sourness (i.e., sugar is not acidic). EDIT: That said, it might be the case that this is a temporal situation. Sugar reduces the perception of sourness, but it could be the case this change is temporary: For example, if the sweetness (sugar) dissipates more quickly than the sourness (acids), you might be left with "more sourness than sweetness" in the aftertaste after some time. That is, you're left with "un-maksked" residual sourness which, though present all along, is more perceptible after the sugar has dissipated. However, all of this is entirely speculation; I have no justification for this, and haven't found any supporting information.

Sweetness is perceived by the presence of sugar (and/or other chemicals that happen to interact in similar ways with sweetness perception). Sugar will also impact mouthfeel.

Bitterness is separate also; see this question on salt and bitterness in coffee.

I don't think there are any chemical changes to the sugar happening in this case.