If R is a regular language, is $R^3= R \circ R \circ R$ also regular?
'$R$' 
 is not used in the literature to indicate languages ​​... generally we use $L$.
Anyway, the "$\circ$" operator indicates the concatenation of two or more languages. Keep in mind that the concatenation of regular languages is also regular: you can proove this by 'linking' the NFA's/DFA's thath recognize them.
In this case you are concatenating a regular language with itself, so the resulting language is also regular.

NB: 
The opposite is not always true: if the concatenation of two languages ​​is regular, this does not mean that the languages ​​themselves are necessarily regular.