Thanks for posting some data. However, it is much harder (at least for me) to extract data from an image than from a text listing. So, here are your sample data shown in a way that should be closer to what people here tempted to play may want to use with their favourite software.

Sugar PlantGroup Site Season
     0 "A" "X" "W"
.00135 "A" "X" "S"
   .22 "A" "Y" "W"
 .5002 "A" "Y" "S"
.02569 "A" "Z" "W"
 1.002 "A" "Z" "S"
    .1 "B" "X" "W"
     0 "B" "X" "S"
   .55 "B" "Y" "W"
     0 "B" "Y" "S"
 .0044 "B" "Z" "W"
 .0005 "B" "Z" "S"
   .22 "C" "X" "W"
.00069 "C" "X" "S"
     0 "C" "Y" "W"
     0 "C" "Y" "S"
  .552 "C" "Z" "W"
  .225 "C" "Z" "S"

This is far short of a complete answer but the listing above could not be fitted into a comment.

Some other comments:

1. The mix of recorded zeros and measured positive values may need biological as well as statistical consideration. Are all zeros just recorded as such or are there instances when zeros are predicted or predictable biologically?

2. Apart from the zeros, there is essentially a 2000-fold variation in sugar, which would itself imply to me analysis on a logarithmic scale.

3. Zeros don't rule out logarithmic scale, as (e.g.) generalized linear models with logarithmic link imply positive means, not that all values are positive. Some experiments with such models were not encouraging. I don't think classical ANOVA implementations are up to this mix of logarithmic scale and zero values without some ad hoc transformation that may raise more questions than it answers.

4. Having plant group, site and season as separate controls seems quite in order scientifically (I am not a biologist, but see loosely similar data quite often), but you need a clever design or a larger dataset to squeeze out a clear picture on all three (not to mention their possible interactions). It is not really clear how large the full dataset is beyond your mention of monthly measurements. If the data are essentially time series, you may need an analysis that matches.

5. 6 months, but grouped here into Winter and Summer. What happened to the other 6 months? You know what that means, but please explain.