On decomposition of bent functions in $8$ variables into the sum of two bent functions

A Boolean function in an even number of variables is called bent if it has maximal nonlinearity. We study the well-known hypothesis about the representation of arbitrary Boolean functions in $n$ variables of degree at most $n/2$ as the sum of two bent functions. We prove that bent functions in $8$ variables of degree at most $3$ can be represented as the sum of two bent functions in $8$ variables. It was shown that all quadratic Boolean functions in an even number of variables $n\geqslant 4$ can be represented as the sum of two bent functions of a special form.