According to the current architectural visions, 6G is expected to host various new demanding use cases like massive twinning, massive robots and cobots, and the Tactile Internet. This complex scenario will pose unprecedented challenges to network management and orchestration, which have required the employment of massive in-network intelligence. In-network intelligence will help 6G to achieve its performance indicators in terms of latency and resilience via prediction and proactive management. However, this will imply the significant increase of energy usage for intelligent operations like data mining and classification, learning, and decision-making. This is in contrast with the 6G objectives of sustainability and significant energy cost reduction. Then, the evaluation of the trade-off between in-network intelligence performance and energy usage has a key role. In this context, a testbed has been constructed to measure the energy cost of in-network intelligence systems, where the power cost of an emulated network system, deployed on the stand-alone host hardware, is measured in real-time. Using a vertical in-network intelligence application, our experiments have shown that the in-network intelligence system uses less power than a traditional centralized system, in turn contributing to higher energy efficiency. With increased in-network intelligence resources, less power is consumed, reaching a maximum reduction of 20 % in our experiments. Additionally, the results show that power savings of in-network intelligence also come from its reduced service time. This article illustrates the advantages of in-network computing to help reducing the energy usage of in-network intelligence while also achieving the 6G performance indicators.