∵△ABC中,AB=AC,D是AB的中点,且DE⊥AB,∴AE=BE,
∵△BCE的周长为8cm,即BE+CE+BC=8cm,
∴AC+BC=8cm…①,
∵AC-BC=2cm…②,
①+②得,2AC=10cm,即AC=5cm,故AB=5cm;