There are 2 train companies operating 7 routes - IC77, ICE10, CNL 1258, ICE12, ICE11, RE3, RE60. The cheapest train costs $33 and is 3h 7min.
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There are 3 ways to travel from Braunschweig to Berlin. 4 buses, 3 trains and 1 by car are possible between the two areas. The by car from Braunschweig to Berlin is the cheapest. The train operated by DB running from Braunschweig to Albrechtshof is the fastest. The train operated by DB running from Weddel (Braunschw) to Berlin Hbf is the most convenient.
It's important to check each mode when booking your ticket so that you can find the best method for you. The cost of each type varies differently, so be sure to use Faretrotter to keep an eye out!