According to the United States Census Bureau, Cambridge has a total area of 1.4 square miles (3.7 km²), of which, 1.4 square miles (3.7 km²) of it is land and 0.70% is water.
As of the census of 2000, there were 2,180 people, 856 households, and 595 families residing in the village. The population density was 1,540.2 people per square mile (592.7/km²). There were 896 housing units at an average density of 633.0 per square mile (243.6/km²). The racial makeup of the village was 98.17% White, 0.78% African American, 0.18% Native American, 0.32% Asian, 0.05% Pacific Islander, and 0.50% from two or more races. Hispanic or Latino of any race were 0.46% of the population.