The original sheet of paper measures 25cm by 20cm, so its area is 25cm * 20cm = «2520=500»500 square cm. A strip 2cm wide is cut from all around the sheet, so the new dimensions of the remaining sheet are (25cm - 2cm - 2cm) by (20cm - 2cm - 2cm), which is 21cm by 16cm. The area of the remaining sheet is 21cm * 16cm = «2116=336»336 square cm. The area of the strip cut out is the difference between the area of the original sheet and the area of the remaining sheet, which is 500 square cm - 336 square cm = «500-336=164»164 square cm. Answer: \boxed{164}.