[noun] + でも何でもない [na-adj] + でも何でもない [i-adj 〜い → 〜く] + も何ともない
でも何でもない and くも何ともない deny something flatly: "not … at all", "nothing of the kind". でも何でもない follows a noun or a な-adjective; くも何ともない is the い-adjective version, with the い changed to く.
The word in front decides, just as it does between ではない and くない. The middle word changes too: 何でも after で, 何とも after く. いい becomes よく, as it does before ない. Both are often written in kana: でもなんでもない, くもなんともない.
Both answer an assumption, spoken or implied: someone thinks it hurt, or that he is your boyfriend, and you deny it outright. The tone is dismissive, sometimes defiant, and both belong to speech and informal writing. The next sentence often says what the thing really is.
Word for word it is "not X, and not anything": the denial throws out the word and everything like it. ではない and ぜんぜん全然きごう〜くない state a plain fact, and they are what a neutral report uses.
These go beyond the plain present.
The final ない changes like any ない: なかった for the past, ありません or ないです for polite speech.
でも何でもなくて, or でも何でもなく in writing, links to a clause that says what the thing is instead.