The cumulene carbenes are important components of hydrocarbon chemistry in low-mass star-forming cores. Here we report the first astronomical detection of the long-chain cumulene carbene H2C6 in the interstellar cloud TMC-1, from observations of two of its rotational transitions: J(K,K') = 7(1,7) --> 6(1,6) at 18.8 GHz and 8(1,8) --> 7(1,7) at 21.5 GHz, using NASA's Deep Space Network 70 m antenna at Goldstone, California. In addition we also observed the shorter cumulene carbene H2C4 at the same position. The fractional abundance of H2C6 relative to H2 is about 4.7 x 10(-11) and that of H2C4 is about 4.1 x 10(-9). The abundance of H2C6 is in fairly good agreement with gas-phase chemical models for young molecular cloud cores, but the abundance of H2C4 is significantly larger than predicted.