  We study symplectic embeddings of ellipsoids into balls. In the main
construction, we show that a given embedding of 2m-dimensional ellipsoids can
be suspended to embeddings of ellipsoids in any higher dimension. In dimension
6,s if the ratio of the areas of any two axes is sufficiently large then the
ellipsoid is flexible in the sense that it fully fills a ball. We also show
that the same property holds in all dimensions for sufficiently thin ellipsoids
E(1,..., a). A consequence of our study is that in arbitrary dimension a ball
can be fully filled by any sufficiently large number of identical smaller
balls, thus generalizing a result of Biran valid in dimension 4.
