A problem regarding the first law of thermodynamics
The question didn't specify which process the given molar heat capacity was specified for. So we will assume that it is molar heat capacity for the first process. The first process is isobaric so $$q=nC_p\,\Delta T$$
You calculated $\Delta T$ correctly. The only mistake you did was assume that the gas was monoatomic. The expression for $\Delta U$ you wrote was $\Delta U=\frac32nR\,\Delta T$. This expression would be correct if this was a monoatomic gas. But we don't know that do we?
The correct expression to use here is $$\Delta U=nC_V\,\Delta T$$
It is given that molar heat capacity for first process (constant pressure) is $C_p=25\ \mathrm{J/(^\circ C\ mol)}$ and  we know that $$C_p=C_V+R$$
So you can calculate the value of $C_V$ and use it to get the value of $\Delta U$ which I calculated to be $$\Delta U=667.2\ \mathrm J$$
Plug this into first law of thermodynamics and you will get the correct answer.
Edit: I used the sign $\Delta U$ for Change in Internal Energy intead of $\Delta E$