Make a drum out of cardboard by using heavy-duty cardboard tubes. Cardboard tubes of various sizes are used in construction to provide cylindrical forms for poured concrete, and these can be modified in order to make impressive-sounding drums.
Another option for making a high-quality cardboard based drum are the large tubes that come in the middle of rolls of carpet. Specifically, these large cardboard rolls can be cut to size to make the Brazilian bass drum known as a Surdo, which provides the booming kick drum used in samba music and other styles.
For the drum skin or drum head portion of your cardboard based percussive instrument, you can use packing or gaffer tape.