Must a teaching be declared ex cathedra to be infallible?
The short answer
No. The teaching that artificial birth control is wrong, for example, is already infallible through the ordinary and universal magisterium. And Vatican II taught that the pope's teaching deserves religious submission of will and intellect even when he does not speak ex cathedra.
Ordinary and universal magisterium
The pope need not proclaim ex cathedra that artificial birth control is wrong; it is already infallible teaching through the ordinary and universal magisterium.
Assent to the pope
Lumen Gentium (25) teaches that loyal submission of will and intellect is owed in a special way to the authentic teaching of the Roman Pontiff even when he does not speak ex cathedra, so that his teaching authority is acknowledged with respect and his decisions sincerely accepted.
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