Is $\{u u^R u : u \in \Sigma^*\}$ context-free?
Based on : Pumping Lemma for Context-Free Languages for reversal language

By @lukas.coenig

{ww$^R$w| w $\in$ {a,b}*} doesn't seem to be a context-free language over $\Sigma$  of length two.

Assuming this language isn't context free over an alphabet of size 2 to prove it also over size of 3.. and so on by induction might be interesting..(and if true by induction than there is probably a better way to prove it)