  We investigate the notion of asymptotic symmetries in classical gravity in
higher even dimensions, with $D = 6$ space-time dimensions as the prototype.
Unlike in four dimensions, certain non-linearities persist which necessitates
the complete non-linear analysis we undertake. We show that the free data is
parametrized by a pair of symmetric trace-free tensors at future (past) null
infinity. This involves a redefinition of the radiative field. We define a
symplectic structure generating the radiative phase space at ${\cal I}^{\pm}$
with appropriate boundary conditions which are preserved by the action of
supertranslations. We derive the charge associated to super-translation vector
fields and this charge matches with that derived using the equations of motion
in the full non-linear theory. We elaborate on the precise relationship between
the super-translation charge, the Bondi mass aspect and the "gravitational
memory" in six space-time dimensions, thus providing the first example of an
infrared triangle in non-linear gravity beyond four dimensions.
