That could be taken two ways:

If you mean the positive even integers themselves are what are to be less than
15, the answer is

2²+4²+6²+8²+10²+12²+14² = 4+16+36+64+100+144+196 = 560

However, if you mean that the squares themselves must be less than 15, then

there is only one square of an even number that is less than 15 and that is 

2² or 4.  That's because the next square of an even integer is 4² or 16, which 
is more than 15.

Edwin