Brandenburg was built on a tract of land called Falling Springs, purchased in 1804 by Solomon Brandenburg. He opened a tavern around which the community grew, and in 1825 the community became the county seat, but the settlement didn't incorporate until March 28 1872.
There were 844 households out of which 33.6% had children under the age of 18 living with them, 43.4% were married couples living together, 15.6% had a female householder with no husband present, and 36.5% were non-families. 32.1% of all households were made up of individuals and 12.9% had someone living alone who was 65 years of age or older. The average household size was 2.32 and the average family size was 2.92.
In the city the population was spread out with 26.2% under the age of 18, 9.6% from 18 to 24, 28.6% from 25 to 44, 20.0% from 45 to 64, and 15.6% who were 65 years of age or older. The median age was 36 years. For every 100 females there were 87.6 males. For every 100 females age 18 and over, there were 82.7 males.
The median income for a household in the city was $36,351, and the median income for a family was $42,950. Males had a median income of $30,565 versus $21,143 for females. The per capita income for the city was $17,863. About 14.4% of families and 15.4% of the population were below the poverty line, including 19.3% of those under age 18 and 19.1% of those age 65 or over.