Living cells are neither perfectly elastic nor liquid and return a viscoelastic response to external stimuli. Nanoindentation provides force-distance curves, allowing the investigation of cell mechanical properties, and yet, these curves can differ from point to point on the cell surface, revealing its inhomogeneous character. In the present work, we propose a mathematical method to estimate both viscoelastic and noise properties of cells as these are depicted on the values of the scaling exponents of relaxation function and power spectral density, respectively. The method uses as input the time derivative of the response force in a nanoindentation experiment. Generalized moments method and/or rescaled range analysis is used to study the resulting time series depending on their nonstationary or stationary nature. We conducted experiments in living Ulocladium chartarum spores. We found that spores in the approaching phase present a viscoelastic behavior with the corresponding scaling exponent in the range 0.25-0.52 and in the retracting phase present a liquid-like behavior with exponents in the range 0.67-0.85. This substantial difference of the scaling exponents in the two phases suggests the formation of biomemory as a response of the spores to the indenting AFM mechanical stimulus. The retracting phase may be described as a process driven by bluish noises, while the approaching one is driven by persistent noise.