Living cells, either prokaryote or eukaryote, can be integrated within whole-cell biochips (WCBCs) for various applications. We investigate WCBCs where information is extracted from the cells via a cascade of biochemical reactions that involve gene expression. The overall biological signal is weak due to small sample volume, low intrinsic cell response, and extrinsic signal loss mechanisms. The low signal-to-noise ratio problem is aggravated during initial detection stages and limits the minimum detectable signal or, alternatively, the minimum detection time. Taking into account the stochastic nature of biochemical process, we find that the signal is accompanied by relatively large noise disturbances. In this work, we use genetically engineered microbe sensors as a model to study the biochips output signal stochastic behavior. In our model, the microbes are designed to express detectable reporter proteins under external induction. We present analytical approximated expressions and numerical simulations evaluating the fluctuations of the synthesized reporter proteins population based on a set of equations modeling a cascade of biochemical and genetic reactions. We assume that the reporter proteins decay more slowly than messenger RNA molecules. We calculate the relation between the noise of the input signal (extrinsic noise) and biochemical reaction statistics (intrinsic noise). We discuss in further details two cases: (1) a cascade with large decay rates of all biochemical reactions compared to the protein decay rate. We show that in this case, the noise amplitude has a positive linear correlation with the number of stages in the cascade. (2) A cascade which includes a stable enzymatic-binding reaction with slow decay rate. We show that in this case, the noise strongly depends on the protein decay rate. Finally, a general observation is presented stating that the noise in whole-cell biochip sensors is determined mainly by the first reactions in the genetic system with weak dependence on the number of stages in the cascade.