Electron beam lithography (EBL) at sub-10 nm resolution is mainly limited by resist contrast and proximity effects. In this work, we investigate the use of a recently developed alumina-based resist as a negative-tone resist for electron EBL at 100 keV and focused helium ion beam lithography (FHIBL). The resist is synthesized using a sol-gel method and turns into a near completely inorganic alumina system when exposed to the electron/ion beam. We first investigate the effect on the resist contrast curve on i) development temperature; ii) stability of the resist after exposure and before post-baking and development; and iii) aging of the resist solution. We demonstrate the patterning of isolated features as small as 6.5 nm using an EBL and 5 nm using FHIBL and a resolution down to 10 nm for FHIB exposed films. Finally, we demonstrate the pattern transfer of 10 nm lines with an aspect ratio of 10 in silicon, using an optimized reactive ion etching process.