Could anybody please tell which one is correct?
The President is going to give speeches in Belgium, in the Netherlands, in Luxembourg and in France
versus
The President is going to give speeches in Belgium, the Netherlands, Luxembourg and France
Could anybody please tell which one is correct?
The President is going to give speeches in Belgium, in the Netherlands, in Luxembourg and in France
versus
The President is going to give speeches in Belgium, the Netherlands, Luxembourg and France
Both are fine. The second is an example of a rhetorical device called "zeugma," in which one word applies to many in a set of parallel constructions. Here you have a set of countries that are all the objects in a prepositional phrase, but the preposition appears only once.
Both forms are correct.
"... in X, in Y, in Z ..." : Multiple IN form is used in two cases:
(A) when somebody wants to emphasis some words. Eg "... in Belgium, in Nederlands, ...".
(B) when somebody is speaking impromptu, and wants time to think between countries. Eg "Well, I know the president will give speeches in Belgium, ... in Nederlands, ... in Luxembourg and .... in France".
"... in X, Y, Z ..." Single IN form is nice&short.
Informational Comment:
When some items require Different Prepositional words ("about", "of", "for", "on", "with", etc), we may see many uses of "in" in the same sentence. Eg. "I write stories in weekly magazines about hunting in Africa, for American audiences "with" an interest in wildlife".
Oxford comma aside, the choice is purely rhetorical, stylistic, rhythmic -- it all depends on how it sounds to you. Do you read your work out loud? That can help you decide. Including the "ins" is more emphatic, to my ear; it highlights the fact that the President is giving a number of speeches and that they are in different countries. But it's all up to you, how you want it to sound.