Is Solar Energy Possible Without Sun?

In general solar energy is dependent on the sun shining.

http://en.wikipedia.org/wiki/Solar_power

Solar = Latin for Sun. So your question is like asking if hydro generation will work without water, or if combustion engine generation will work without fuel. "Solar energy" just means energy generated by the sun.

There are however several TYPES of "solar energy": solar photovoltaic energy, which converts sun LIGHT directly into electricity; solar THERMAL energy, which converts solar radiation into heat, which can be used directly as heat or used to create steam to generate electricity and if you think about it, hydro power is actually a form of "solar energy" in that the sun evaporates water, which collects in the sky and falls as rain, then turns turbine generators. So to that end, there is always a bit of "solar energy" taking place all the time in one way or another. A "warm day" implies daytime, which means the sun is out, but presumably you are referring to it being obscured by clouds. In that case, yes, all forms of "solar energy" are still taking place, just at reduced rates.

actually most panels perform better when they are not hot. but the panel needs photons to strike them at favorable angles in order for the panel to produce at optimal levels, no photons = no generation of DC current

A much lower output power is possible dependent upon the phases of the moon.

For some reason, output also falls off with cloud cover and during eclipses.

...and at night.

A properly sized and engineered system stores energy to provide 24/7.....Generally speaking, that storage medium is batteries....Depending on how much storage you have(batteries) then your solar panel array is sized to not only meet the load but to recharge your battery bank as well.....

http://en.wikipedia.org/wiki/Photovoltaic_system

By mounting a reflector on a satellite in night,sunlight could be focussed on a selected plot of land on earth. I believe that Russians demonstrated it in Paris. The other method is fixing solar panels in homes/offices to catch waste light falling outside working areas.