Put epoxy between the inner(the short new tube) and outer (original) tube. Be sure the sand both surfaces and use an epoxy made to glue aluminum. Epoxy made to glue aluminum is usally grey or black and says something about being special for glueing metals.

If you want to be fancy (or if this splice breaks) take some 3 in wide fiberglass tape and make a fiberglass tube over the break in addition to the tube on the inside. Use a little tape to tape the end of the fiberglass tape to the aluminum. Wrap the fiberglass around aluminum, wetting it with epoxy as you wrap it. Brush just enough epoxy on the fiberglass for it to look transparent but not enough for it to drip onto the ground. Be sure to wrap it tight. The fiberglass will need to be 1/16-1/8 thick.

When you are finished, paint it white, drill and rivet through the fiberglass, orginal and splice tube. The reason for riveting is, the epoxy bond between the aluminum and the fiberglass will break.

By the way, where are you?
Good Luck