I've been looking at my used Colgate toothpaste tube and thinking it might be aluminum...but it's not: it's a laminate. Which isn't recyclable anywhere I can find, unless your laminate tube is from Tom's of maine and you wish to mail it back to them.
You can get crafty with the laminate, if you had the desire: make a colgate toothbrush holder from toothpaste tubes
You have to save up five tubes, and it's not the most glamorous bathroom decor. Would be cute in a kid's bathroom i think, or an adult's retrostyle bath.
This site says one billion tubes are tossed in landfills each year! recycling toothpast tubes