In the One Punch Man Wiki, the page about Genos says:
Genos is a 19 year old cyborg and the disciple of Saitama.
He has an entirely mechanical body in the model of a handsome young man. His face and ears look like that of a normal human, made of an artificial skin material, and his eyes have black sclera with yellow irises.
Now, if we look at some definitions for the word cyborg:
1. "a person whose physiological functioning is aided by or dependent upon a mechanical or electronic device."
2. "a person whose body contains mechanical or electrical devices and whose abilities are greater than the abilities of normal humans"
3. "an organism, often a human, that has certain physiological processes enhanced or controlled by mechanical or electronic devices, especially when they are integrated with the nervous system."
4. "a living being whose powers are enhanced by computer implants or mechanical body parts"
5. "a human being whose body has been taken over in whole or in part by electromechanical devices; "a cyborg is a cybernetic organism"
Source for definitions no. 3, 4, 5 :http://www.thefreedictionary.com/cyborg
6. "a cyborg (short for "cybernetic organism") is a being with both organic and biomechatronic body parts."
Based on definitons no. 1, 2, 3, 4 and 6 we can positively say that Genos is not a cyborg for "he has an entirely mechanical body" (first paragraph) and does not contain any human flesh or tissue, contrary to definiton no.6 : "a being with both organic and biomechatronic body parts."
In definition no. 5 it says "in whole or in part" giving a small possibility to say that he is a cyborg but it is rather an affirmation without a solid base.
I think that he says he says he is a "cyborg" because it sounds better and cooler than "robot". His name in the Hero Association " Demon Cyborg (鬼サイボーグ, Oni Saibōgu)" sounds better than "Demon Robot". Or maybe it was an action made deliberately by the author himself.
In the end, it is the right of everyone to call him as they wish, this fact not being such an influential aspect of the story.