If the mean and variance of the data $$65, 68, 58, 44, 48, 45, 60, \alpha, \beta, 60$$ where $$\alpha > \beta$$ are $$56$$ and $$66.2$$ respectively, then $$\alpha^2 + \beta^2$$ is equal to _______

Sum $$= 65+68+58+44+48+45+60+\alpha+\beta+60 = 448+\alpha+\beta$$. Mean=56: $$448+\alpha+\beta=560$$, $$\alpha+\beta=112$$.

Σx²=65²+68²+...+60²+α²+β²=sum of known squares+α²+β². Known: $$4225+4624+3364+1936+2304+2025+3600+3600=25678$$.

Variance=66.2: Σx²/10 - 56² = 66.2. Σx²=10(3136+66.2)=32022.

α²+β²=32022-25678=6344. The answer is $$\boxed{6344}$$.