An unknown absorber near the cloud-top level of Venus generates a broad absorption feature from the ultraviolet (UV) to visible, peaking around 360 nm, and therefore plays a critical role in the solar energy absorption. We present a quantitative study of the variability of the cloud albedo at 365 nm and its impact on Venus's solar heating rates based on an analysis of Venus Express and Akatsuki UV images and Hubble Space Telescope and MESSENGER UV spectral data; in this analysis, the calibration correction factor of the UV images of Venus Express (Venus Monitoring Camera) is updated relative to the Hubble and MESSENGER albedo measurements. Our results indicate that the 365 nm albedo varied by a factor of 2 from 2006 to 2017 over the entire planet, producing a 25%-40% change in the low-latitude solar heating rate according to our radiative transfer calculations. Thus, the cloud-top level atmosphere should have experienced considerable solar heating variations over this period. Our global circulation model calculations show that this variable solar heating rate may explain the observed variations of zonal wind from 2006 to 2017. Overlaps in the timescale of the long-term UV albedo and the solar activity variations make it plausible that solar extreme UV intensity and cosmic-ray variations influenced the observed albedo trends. The albedo variations might also be linked with temporal variations of the upper cloud SO2 gas abundance, which affects the H2SO4-H2O aerosol formation.