Recent nuclear magnetic resonance (NMR) measurements revealed the coexistence of stripe-type antiferromagnetic (AFM) and ferromagnetic (FM) spin correlations in both the hole- and electron-doped BaFe$_2$As$_2$ families of iron-pnictide superconductors by a Korringa ratio analysis. Motivated by the NMR work, we investigate the possible existence of FM fluctuations in another iron pnictide superconducting family, Ca(Fe$_{1-x}$Co$_x$)$_2$As$_2$. We re-analyzed our previously reported data in terms of the Korringa ratio and found clear evidence for the coexistence of stripe-type AFM and FM spin correlations in the electron-doped CaFe$_2$As$_2$ system. These NMR data indicate that FM fluctuations exist in general in iron-pnictide superconducting families and thus must be included to capture the phenomenology of the iron pnictides.